{"title":"Differential and Riemannian geometry Books","description":"","products":[{"product_id":"constrained-willmore-surfaces-9781108794428","title":"Constrained Willmore Surfaces","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eFrom Bäcklund to Darboux, this monograph presents a comprehensive journey through the transformation theory of constrained Willmore surfaces, a topic of great importance in modern differential geometry and, in particular, in the field of integrable systems in Riemannian geometry. The first book on this topic, it discusses in detail a spectral deformation, Bäcklund transformations and Darboux transformations, and proves that all these transformations preserve the existence of a conserved quantity, defining, in particular, transformations within the class of constant mean curvature surfaces in 3-dimensional space-forms, with, furthermore, preservation of both the space-form and the mean curvature, and bridging the gap between different approaches to the subject, classical and modern. Clearly written with extensive references, chapter introductions and self-contained accounts of the core topics, it is suitable for newcomers to the theory of constrained Wilmore surfaces. Many detailed comp\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction; 1. A bundle approach to conformal surfaces in space-forms; 2. The mean curvature sphere congruence; 3. Surfaces under change of flat metric connection; 4. Willmore surfaces; 5. The Euler–Lagrange constrained Willmore surface equation; 6. Transformations of generalized harmonic bundles and constrained Willmore surfaces; 7. Constrained Willmore surfaces with a conserved quantity; 8. Constrained Willmore surfaces and the isothermic surface condition; 9. The special case of surfaces in 4-space; Appendix A. Hopf differential and umbilics; Appendix B. Twisted vs. untwisted Bäcklund transformation parameters; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738537800023,"sku":"9781108794428","price":55.09,"currency_code":"GBP","in_stock":true}]},{"product_id":"from-differential-geometry-to-non-commutative-geometry-and-topology-9783030284350","title":"From Differential Geometry to Non-commutative","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book aims to provide a friendly introduction to non-commutative geometry. It studies index theory from a classical differential geometry perspective up to the point where classical differential geometry methods become insufficient. It then presents non-commutative geometry as a natural continuation of classical differential geometry. It thereby aims to provide a natural link between classical differential geometry and non-commutative geometry. The book shows that the index formula is a topological statement, and ends with non-commutative topology.\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“The present book is well written. It is very useful to researchers in differential geometry who are interested in non-commutative geometry. It provides motivations for tudying non commutative geometry.” (Ion Mihai, zbMATH 1458.58001, 2021)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Part I Spaces, bundles and characteristic classes in differential geometry.- 2. Part II Non-commutative differential geometry.- 3. Part III Index Theorems.- 4. Part IV Prospects in Index Theory. Part V.- 5. Non-commutative topology.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743028556119,"sku":"9783030284350","price":104.49,"currency_code":"GBP","in_stock":true}]},{"product_id":"introduction-to-geometric-control-9783031020728","title":"Introduction to Geometric Control","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis text is an enhanced, English version of the Russian edition, published in early 2021 and is appropriate for an introductory course in geometric control theory. The concise presentation provides an accessible treatment of the subject for advanced undergraduate and graduate students in theoretical and applied mathematics, as well as to experts in classic control theory for whom geometric methods may be introduced. Theory is accompanied by characteristic examples such as stopping a train, motion of mobile robot, Euler elasticae, Dido's problem, and rolling of the sphere on the plane. Quick foundations to some recent topics of interest like control on Lie groups and sub-Riemannian geometry are included. Prerequisites include only a basic knowledge of calculus, linear algebra, and ODEs; preliminary knowledge of control theory is not assumed. The applications problems-oriented approach discusses core subjects and encourages the reader to solve related challenges independently. Highly-motivated readers can acquire working knowledge of geometric control techniques and progress to studying control problems and more comprehensive books on their own. Selected sections provide exercises to assist in deeper understanding of the material.\u003c\/p\u003e\u003cp\u003eControllability and optimal control problems are considered for nonlinear nonholonomic systems on smooth manifolds, in particular, on Lie groups. For the controllability problem, the following questions are considered: controllability of linear systems, local controllability of nonlinear systems, Nagano–Sussmann Orbit theorem, Rashevskii–Chow theorem, Krener's theorem. For the optimal control problem, Filippov's theorem is stated, invariant formulation of Pontryagin maximum principle on manifolds is given, second-order optimality conditions are discussed, and the sub-Riemannian problem is studied in detail. Pontryagin maximum principle is proved for sub-Riemannian problems, solution to the sub-Riemannian problems on the Heisenberg group, the group of motions of the plane, and the Engel group is described.\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Introduction.- 2. Controllability problem.- 3. Optimal control problem.- 4. Solution to optimal control problems.- 5. Conclusion.- A. Elliptic integrals, functions and equation of pendulum.- Bibliography and further reading.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743065420119,"sku":"9783031020728","price":43.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031020728.jpg?v=1720063957"},{"product_id":"linear-fractional-transformations-an-illustrated-introduction-9783031250019","title":"Linear Fractional Transformations: An Illustrated","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe principle aim of this unique text is to illuminate the beauty of the subject both with abstractions like proofs and mathematical text, and with visuals, such as abundant illustrations and diagrams. With few mathematical prerequisites, geometry is presented through the lens of linear fractional transformations. The exposition is motivational and the well-placed examples and exercises give students ample opportunity to pause and digest the material. The subject builds from the fundamentals of Euclidean geometry, to inversive geometry, and, finally, to hyperbolic geometry at the end. Throughout, the author aims to express the underlying philosophy behind the definitions and mathematical reasoning. \u003c\/p\u003e This text may be used as primary for an undergraduate geometry course or a freshman seminar in geometry, or as supplemental to instructors in their undergraduate courses in complex analysis, algebra, and number theory. There are elective courses that bring together seemingly disparate topics and this text would be a welcome accompaniment.\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eMotivation.- I Euclidean and Inversive Geometry.- Euclidean Isometries and Similarities.- Inversive Geometry.- Applications of Inversive Geometry.- II Non-Euclidean Geometry.- Spherical Geometry.- Appendix: Set Theory.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743077183831,"sku":"9783031250019","price":38.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031250019.jpg?v=1720064009"},{"product_id":"differential-geometry-connections-curvature-and-characteristic-classes-9783319550824","title":"Differential Geometry: Connections, Curvature,","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of  de Rham cohomology is required for the last third of the text.\u003cp\u003ePrerequisite material is contained in author's text \u003ci\u003eAn Introduction to Manifolds\u003c\/i\u003e, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included.\u003c\/p\u003e\u003cp\u003eDifferential geometry, as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields.  The field has even found applications to group theory as in Gromov's work and to probability theory as in Diaconis's work. It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The textbook is a concise and well organized treatment of characteristic classes on principal bundles. It is characterized by a right balance between rigor and simplicity. It should be in every mathematician's arsenal and take its place in any mathematical library.” (Nabil L. Youssef, zbMATH 1383.53001, 2018)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- Chapter 1. Curvature and Vector Fields.- 1. Riemannian Manifolds.- 2. Curves.- 3. Surfaces in Space.- 4. Directional Derivative in Euclidean Space.- 5. The Shape Operator.- 6. Affine Connections.- 7. Vector Bundles.- 8. Gauss's Theorema Egregium.- 9. Generalizations to Hypersurfaces in Rn+1.- Chapter 2. Curvature and Differential Forms.- 10. Connections on a Vector Bundle.- 11. Connection, Curvature, and Torsion Forms.- 12. The Theorema Egregium Using Forms.- Chapter 3. Geodesics.- 13. More on Affine Connections.- 14. Geodesics.- 15. Exponential Maps.- 16. Distance and Volume.- 17. The Gauss-Bonnet Theorem.- Chapter 4. Tools from Algebra and Topology.- 18. The Tensor Product and the Dual Module.- 19. The Exterior Power.- 20. Operations on Vector Bundles.- 21. Vector-Valued Forms.- Chapter 5. Vector Bundles and Characteristic Classes.- 22. Connections and Curvature Again.- 23. Characteristic Classes.- 24. Pontrjagin Classes.- 25. The Euler Class and Chern Classes.- 26. Some Applications of Characteristic Classes.- Chapter 6. Principal Bundles and Characteristic Classes.- 27. Principal Bundles.- 28. Connections on a Principal Bundle.- 29. Horizontal Distributions on a Frame Bundle.- 30. Curvature on a Principal Bundle.- 31. Covariant Derivative on a Principal Bundle.- 32. Character Classes of Principal Bundles.- A. Manifolds.- B. Invariant Polynomials.- Hints and Solutions to Selected End-of-Section Problems.- List of Notations.- References.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743098351959,"sku":"9783319550824","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"introduction-to-riemannian-manifolds-9783319917542","title":"Introduction to Riemannian Manifolds","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“One interesting aspect of the book is the decision of which audience to target it towards. … Overall, this would make a very appropriate text for a graduate course, or a programme of individual study in Riemannian geometry, whether to give a thorough treatment of the fundamentals, or to introduce the more advanced topics in global geometry.” (Robert J. Low, Mathematical Reviews, November, 2019)\u003cbr\u003e“This material is carefully developed and several useful examples and exercises are included in each chapter. The reviewer’s belief is that this excellent edition will become soon a standard text for several graduate courses as well as an frequent citation in articles.” (Mircea Crâşmăreanu, zbMATH 1409.53001, 2019)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- 1. What Is Curvature?.- 2. Riemannian Metrics.- 3. Model Riemannian Manifolds.- 4. Connections.- 5. The Levi-Cevita Connection.- 6. Geodesics and Distance.- 7. Curvature.- 8. Riemannian Submanifolds.- 9. The Gauss–Bonnet Theorem.- 10. Jacobi Fields.- 11. Comparison Theory.- 12. Curvature and Topology.- Appendix A: Review of Smooth Manifolds.- Appendix B:  Review of Tensors.- Appendix C: Review of Lie Groups.- References.- Notation Index.- Subject Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743109263703,"sku":"9783319917542","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"a-brief-introduction-to-berezin-toeplitz-operators-on-compact-kahler-manifolds-9783319946818","title":"A Brief Introduction to Berezin–Toeplitz","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis text provides a comprehensive introduction to Berezin–Toeplitz operators on compact Kähler manifolds. The heart of the book is devoted to a proof of the main properties of these operators which have been playing a significant role in various areas of mathematics such as complex geometry, topological quantum field theory, integrable systems, and the study of links between symplectic topology and quantum mechanics. The book is carefully designed to supply graduate students with a unique accessibility to the subject. The first part contains a review of relevant material from complex geometry. Examples are presented with explicit detail and computation; prerequisites have been kept to a minimum. Readers are encouraged to enhance their understanding of the material by working through the many straightforward exercises. \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“The book … represents an essential prerequisite for anyone who wants to work in the field. The author have managed to make it readable by non-specialists.” (Béchir Dali, zbMATH 1452.32002, 2021)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- 1. Introduction.- 2. A short introduction to Kähler manifolds.- 3. Complex line bundles with connections.- 4. Quantization of compact Kähler manifolds.- 5. Berezin–Toeplitz operators.- 6. Schwartz kernels.- 7. Asymptotics of the projector Pi_k.- 8. Proof of product and commutator estimates.- 9. Coherent states and norm correspondence.- A. The circle bundle point of view.- Bibliography.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743110639959,"sku":"9783319946818","price":49.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319946818.jpg?v=1720064156"},{"product_id":"a-visual-introduction-to-differential-forms-and-calculus-on-manifolds-9783319969916","title":"A Visual Introduction to Differential Forms and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and enable readers to visualize the concepts being discussed. The author gradually builds up to the basic ideas and concepts so that definitions, when made, do not appear out of nowhere, and both the importance and role that theorems play is evident as or before they are presented. With a clear writing style and easy-to- understand motivations for each topic, this book is primarily aimed at second- or third-year undergraduate math and physics students with a basic knowledge of vector calculus and linear algebra.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e “The reviewer recommends young mathematics and physics majors to open the book and to keep it on their bookshelves. Indeed, the reviewer even envies young students who can study differential forms with such a fascinating book.” (Hirokazu Nishimura, zbMath 1419.58001, 2019)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e  ","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":48743111459159,"sku":"9783319969916","price":53.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319969916.jpg?v=1720064159"},{"product_id":"optimal-transport-old-and-new-9783540710493","title":"Optimal Transport: Old and New","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eAt the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003ePhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject. \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003e\"The book is aimed to old and new problems of optimal transport. … This meticulous work is based on very large bibliography … that is converted into a very valuable monograph that presents many statements and theorems written specifically for this approach, complete and self-contained proofs of the most important results, and extensive bibliographical notes.\" (Mihail Voicu, Zentralblatt MATH, Vol. 1156, 2009)\u003c\/p\u003e\u003cp\u003e“This book wins the challenge to give a new and broad perspective on the multifacet topic of the optimal mass transport. … Besides extensive and accurate references therein the reader will find comments on related questions barely touched upon in the main text as well as lively presentations on how ideas and results have developed. This book should prove useful both to the expert and to the beginner looking for a reference text on the subject.” (Dario Cordero Erausquin, Mathematical Reviews, Issue 2010 f)\u003c\/p\u003e\u003cp\u003e“The book is an in-depth, modern, clear exposition of the advanced theory of optimal transport, and it tries to put together in a unified way almost all the recent developments of the theory. … the book is extremely well written and very pleasant to read. … I strongly recommend this excellent book to every researcher or graduate student in the field of optimal transport. … of interest to many mathematicians in different areas, who are simply interested in having an overview of the subject.” (Alessio Figalli, Bulletin of the American Mathematical Society, Vol. 47 (4), February, 2010)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eCouplings and changes of variables.- Three examples of coupling techniques.- The founding fathers of optimal transport.- Qualitative description of optimal transport.- Basic properties.- Cyclical monotonicity and Kantorovich duality.- The Wasserstein distances.- Displacement interpolation.- The Monge—Mather shortening principle.- Solution of the Monge problem I: global approach.- Solution of the Monge problem II: Local approach.- The Jacobian equation.- Smoothness.- Qualitative picture.- Optimal transport and Riemannian geometry.- Ricci curvature.- Otto calculus.- Displacement convexity I.- Displacement convexity II.- Volume control.- Density control and local regularity.- Infinitesimal displacement convexity.- Isoperimetric-type inequalities.- Concentration inequalities.- Gradient flows I.- Gradient flows II: Qualitative properties.- Gradient flows III: Functional inequalities.- Synthetic treatment of Ricci curvature.- Analytic and synthetic points of view.- Convergence of metric-measure spaces.- Stability of optimal transport.- Weak Ricci curvature bounds I: Definition and Stability.- Weak Ricci curvature bounds II: Geometric and analytic properties.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":48743131283799,"sku":"9783540710493","price":113.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"differential-geometry-9780486667218","title":"Differential Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAn introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form, but with many explanatory details, figures, and examples, and in a manner that conveys the theoretical and practical importance of the different concepts, methods, and results involved. With problems and solutions. Includes 99 illustrations.","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48864740409687,"sku":"9780486667218","price":14.39,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486667218.jpg?v=1722273025"},{"product_id":"differential-geometry-of-curves-and-surfaces-9780486806990","title":"Differential Geometry of Curves and Surfaces","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eOne of the most widely used texts in its field, this volume has been continuously in print since its initial 1976 publication. The clear, well-written exposition is enhanced by many examples and exercises, some with hints and answers. Prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables.","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48864742998359,"sku":"9780486806990","price":26.79,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486806990.jpg?v=1722273036"},{"product_id":"morse-theory-9780691080086","title":"Morse Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eOne classical application of Morse theory includes the attempt to understand, with only limited information, the large-scale structure of an object. This kind of problem occurs in mathematical physics, dynamic systems, and mechanical engineering. This book offers an exposition of Morse theory by John Milnor, recipient of the Fields Medal in 1962.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"John Milnor, Winner of the 2011 Abel Prize from the Norwegian Academy of Science and Letters\"\u003cbr\u003e\"John Willard Milnor, Winner of the 2011 Leroy P. Steele Prize for Lifetime Achievement, American Mathematical Society\"\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*Frontmatter, pg. i*PREFACE, pg. v*CONTENTS, pg. vii*PART I. NON-DEGENERATE SMOOTH FUNCTIONS ON A MANIFOLD, pg. 1*PART II. A RAPID COURSE IN RIEMANNIAN GEOMETRY, pg. 43*PART III. THE CALCULUS OF VARIATIONS APPLIED TO GEODESICS, pg. 67*PART IV. APPLICATIONS TO LIE GROUPS AND SYMMETRIC SPACES, pg. 109*APPENDIX. THE HOMOTOPY TYPE OF A MONOTONE UNION, pg. 149","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865516618071,"sku":"9780691080086","price":59.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691080086.jpg?v=1722274345"},{"product_id":"general-relativity-the-theoretical-minimum-9781541601772","title":"General Relativity: The Theoretical Minimum","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eThe latest volume in the \u003ci\u003eNew York Times–\u003c\/i\u003ebestselling physics series explains Einstein’s masterpiece: the general theory of relativity\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eHe taught us classical mechanics, quantum mechanics, and special relativity. Now, physicist Leonard Susskind, assisted by a new collaborator, André Cabannes, returns to tackle Einstein’s general theory of relativity. Starting from the equivalence principle and covering the necessary mathematics of Riemannian spaces and tensor calculus, Susskind and Cabannes explain the link between gravity and geometry. They delve into black holes, establish Einstein field equations, and solve them to describe gravity waves. The authors provide vivid explanations that, to borrow a phrase from Einstein himself, are as simple as possible (but no simpler). \u003c\/p\u003e\u003cp\u003eAn approachable yet rigorous introduction to one of the most important topics in physics, \u003ci\u003eGeneral Relativity\u003c\/i\u003e is a must-read for anyone who wants a deeper knowledge of the universe’s real structure.  \u003c\/p\u003e","brand":"Basic Books","offers":[{"title":"Default Title","offer_id":48867547283799,"sku":"9781541601772","price":24.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781541601772.jpg?v=1722283813"},{"product_id":"an-introduction-to-smooth-manifolds-9789819905676","title":"An Introduction to Smooth Manifolds","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e1. Calculus on Rn.- 2. Manifold Theory.- 3. Differential Forms.- 4. Lie Group.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":48890227851607,"sku":"9789819905676","price":47.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789819905676.jpg?v=1722558056"},{"product_id":"geometry-of-black-holes-9780198873204","title":"Geometry of Black Holes","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eBlack holes present one of the most fascinating predictions of Einstein''s general theory of relativity. There is strong evidence of their existence through observation of active galactic nuclei, including the centre of our galaxy, observations of gravitational waves, and others.There exists a large scientific literature on black holes, including many excellent textbooks at various levels. However, most of these steer clear from the mathematical niceties needed to make the theory of black holes a mathematical theory. Those which maintain a high mathematical standard are either focused on specific topics, or skip many details. The objective of this book is to fill this gap and present a detailed, mathematically oriented, extended introduction to the subject.The book provides a wide background to the current research on all mathematical aspects of the geometry of black hole spacetimes.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eWritten with a high standard of rigor and care, with very good treatments of many topics that are hard to find elsewhere. * Robert Wald, University of Chicago *\u003cbr\u003eIncluding some very interesting and unique material, the book is written in a manner that will be accessible for students, and provide a valuable resource for experts working in mathematical general relativity. * Greg Galloway, University of Miami *\u003cbr\u003eThis text is an excellent research level monograph exploring the detailed and rich structure of black holes in mathematical physics. * Kymani Armstrong-Williams, Physics Book Reviews *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePART I GLOBAL LORENTZIAN GEOMETRY 1: Basic Notions 2: Elements of causality 3: Some applications PART II BLACK HOLES 4: An introduction to black holes 5: Further selected solutions 6: Extensions, conformal diagrams 7: Projection diagrams 8: Dynamical black holes","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":49083402092887,"sku":"9780198873204","price":37.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198873204.jpg?v=1725548824"},{"product_id":"selected-works-of-isadore-singer-volume-2-index-theory-9781571464064","title":"Selected Works of Isadore Singer: Volume 2: Index","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis collection presents the major mathematical works of Isadore Singer, selected by Singer himself, and organized thematically into three volumes:\u003cul\u003e\n\u003cli\u003e1. Functional analysis, differential geometry and eigenvalues\u003c\/li\u003e\n\u003cli\u003e2. Index theory\u003c\/li\u003e\n\u003cli\u003e3. Gauge theory and physics\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003eEach volume begins with a commentary (and in the first volume, a short biography of Singer), and then presents the works on its theme in roughly chronological order.","brand":"International Press of Boston Inc","offers":[{"title":"Default Title","offer_id":49084144091479,"sku":"9781571464064","price":40.8,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781571464064.jpg?v=1725551192"},{"product_id":"conformal-differential-geometry-and-its-generalizations-9780471149583","title":"Conformal Differential Geometry and Its","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eComprehensive coverage of the foundations, applications, recent developments, and future of conformal differential geometry. Conformal Differential Geometry and Its Generalizations systematically presents the foundations and manifestations of conformal differential geometry.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eConformal and Pseudoconformal Spaces.\u003cbr\u003e \u003cbr\u003e Hypersurfaces in Conformal Spaces.\u003cbr\u003e \u003cbr\u003e Submanifolds in Conformal and Pseudoconformal Spaces.\u003cbr\u003e \u003cbr\u003e Conformal Structures on a Differentiable Manifold.\u003cbr\u003e \u003cbr\u003e The Four-Dimensional Conformal Structures.\u003cbr\u003e \u003cbr\u003e Geometry of the Grassmann Manifold.\u003cbr\u003e \u003cbr\u003e Manifolds Endowed with Almost Grassmann Structures.\u003cbr\u003e \u003cbr\u003e Bibliography.\u003cbr\u003e \u003cbr\u003e Symbols Frequently Used.\u003cbr\u003e \u003cbr\u003e Indexes.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402498908503,"sku":"9780471149583","price":179.06,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471149583.jpg?v=1730480596"},{"product_id":"an-introduction-to-integration-and-measure-theory-9780471595182","title":"An Introduction to Integration and Measure Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book describes integration and measure theory for readers interested in analysis, engineering, and economics. It gives a systematic account of Riemann-Stieltjes integration and deduces the Lebesgue-Stieltjes measure from the Lebesgue-Stieltjes integral.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eLIMITATIONS OF THE RIEMANN INTEGRAL.\u003cbr\u003e \u003cbr\u003e Limits of Integrals and Integrability.\u003cbr\u003e \u003cbr\u003e Expectations in Probability Theory.\u003cbr\u003e \u003cbr\u003e RIEMANN-STIELTJES INTEGRALS.\u003cbr\u003e \u003cbr\u003e Riemann-Stieltjes Integrals: Introduction.\u003cbr\u003e \u003cbr\u003e Characterization of Riemann-Stieltjes Integrability.\u003cbr\u003e \u003cbr\u003e Continuous Linear Functionals on C[a,b].\u003cbr\u003e \u003cbr\u003e Riemann-Stieltjes Integrals: Further Properties.\u003cbr\u003e \u003cbr\u003e LEBESGUE-STIELTJES INTEGRALS.\u003cbr\u003e \u003cbr\u003e The Extension of the Riemann-Stieltjes Integral.\u003cbr\u003e \u003cbr\u003e Lebesgue-Stieltjes Integrals.\u003cbr\u003e \u003cbr\u003e MEASURE THEORY.\u003cbr\u003e \u003cbr\u003e sigma-Algebras and Algebras of Sets.\u003cbr\u003e \u003cbr\u003e Measurable Functions.\u003cbr\u003e \u003cbr\u003e Measures.\u003cbr\u003e \u003cbr\u003e Lebesgue-Stieltjes Measures.\u003cbr\u003e \u003cbr\u003e THE ABSTRACT LEBESGUE INTEGRAL.\u003cbr\u003e \u003cbr\u003e The Integral Associated with a Measure Space.\u003cbr\u003e \u003cbr\u003e The Lebesgue Spaces and Norms.\u003cbr\u003e \u003cbr\u003e Absolutely Continuous Measures.\u003cbr\u003e \u003cbr\u003e Linear Functionals on the Lebesgue Spaces.\u003cbr\u003e \u003cbr\u003e Product Measures and Fubini's Theorem.\u003cbr\u003e \u003cbr\u003e Lebesgue Integration and Measures on R?n.\u003cbr\u003e \u003cbr\u003e Signed Measures and Complex Measures.\u003cbr\u003e \u003cbr\u003e Differentiation.\u003cbr\u003e \u003cbr\u003e Convergence of Sequences of Functions.\u003cbr\u003e \u003cbr\u003e Measures on Locally Compact Spaces.\u003cbr\u003e \u003cbr\u003e Hausdorff Measures and Dimension.\u003cbr\u003e \u003cbr\u003e Lorentz Spaces.\u003cbr\u003e \u003cbr\u003e Appendices.\u003cbr\u003e \u003cbr\u003e Indexes.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402641744215,"sku":"9780471595182","price":165.56,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471595182.jpg?v=1730481070"},{"product_id":"characteristic-classes-9780691081229","title":"Characteristic Classes","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"John Milnor, Winner of the 2011 Abel Prize from the Norwegian Academy of Science and Letters\"\u003cbr\u003e\"John Willard Milnor, Winner of the 2011 Leroy P. Steele Prize for Lifetime Achievement, American Mathematical Society\"\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*Frontmatter, pg. i*Preface, pg. v*Contents, pg. vii* 1. Smooth Manifolds, pg. 1* 2. Vector Bundles, pg. 13* 3. Constructing New Vector Bundles Out of Old, pg. 25* 4. Stiefel-Whitney Classes, pg. 37* 5. Grassmann Manifolds and Universal Bundles, pg. 55* 6. A Cell Structure for Grassmann Manifolds, pg. 73* 7. The Cohomology Ring H*(Gn; Z\/2), pg. 83* 8. Existence of Stiefel-Whitney Classes, pg. 89* 9. Oriented Bundles and the Euler Class, pg. 95* 10. The Thom Isomorphism Theorem, pg. 105* 11. Computations in a Smooth Manifold, pg. 115* 12. Obstructions, pg. 139* 13. Complex Vector Bundles and Complex Manifolds, pg. 149* 14. Chern Classes, pg. 155* 15. Pontrjagin Classes, pg. 173* 16. Chern Numbers and Pontrjagin Numbers, pg. 183* 17. The Oriented Cobordism Ring OMEGA*, pg. 199* 18. Thom Spaces and Transversality, pg. 205* 19. Multiplicative Sequences and the Signature Theorem, pg. 219* 20. Combinatorial Pontrjagin Classes, pg. 231*Epilogue, pg. 249*Appendix A: Singular Homology and Cohomology, pg. 257*Appendix B: Bernoulli Numbers, pg. 281*Appendix C: Connections, Curvature, and Characteristic Classes, pg. 289*Bibliography, pg. 315*Index, pg. 325","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403712242007,"sku":"9780691081229","price":92.65,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691081229.jpg?v=1730484332"},{"product_id":"the-decomposition-of-global-conformal-invariants-9780691153476","title":"The Decomposition of Global Conformal Invariants","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAddresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*FrontMatter, pg. i*Contents, pg. v*Acknowledgments, pg. vii*1. Introduction, pg. 1*2. An Iterative Decomposition of Global Conformal Invariants: The First Step, pg. 19*3. The Second Step: The Fefferman-Graham Ambient Metric and the Nature of the Decomposition, pg. 71*4. A Result on the Structure of Local Riemannian Invariants: The Fundamental Proposition, pg. 135*5. The Inductive Step of the Fundamental Proposition: The Simpler Cases, pg. 211*6. The Inductive Step of the Fundamental Proposition: The Hard Cases, Part I, pg. 297*7. The Inductive Step of the Fundamental Proposition: The Hard Cases, Part II, pg. 361*A. Appendix, pg. 403*Bibliography, pg. 443*Index of Authors and Terms, pg. 447*Index of Symbols, pg. 449","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403789050199,"sku":"9780691153476","price":170.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691153476.jpg?v=1730484546"},{"product_id":"hypoanalytic-structures-9780691606705","title":"HypoAnalytic Structures","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eIn Hypo-Analytic Structures Franois Treves provides a systematic approach to the study of the differential structures on manifolds defined by systems of complex vector fields. Serving as his main examples are the elliptic complexes, among which the De Rham and Dolbeault are the best known, and the tangential Cauchy-Riemann operators. Basic geometri\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePrefaceIFormally and Locally Integrable Structures. Basic Definitions3I.1Involutive systems of linear PDE defined by complex vector fields. Formally and locally integrable structures5I.2The characteristic set. Partial classification of formally integrable structures11I.3Strongly noncharacteristic, totally real, and maximally real submanifolds16I.4Noncharacteristic and totally characteristic submanifolds23I.5Local representations27I.6The associated differential complex32I.7Local representations in locally integrable structures39I.8The Levi form in a formally integrable structure46I.9The Levi form in a locally integrable structure49I.10Characteristics in real and in analytic structures56I.11Orbits and leaves. Involutive structures of finite type63I.12A model case: Tube structures68IILocal Approximation and Representation in Locally Integrable Structures73II.1The coarse local embedding76II.2The approximation formula81II.3Consequences and generalizations86II.4Analytic vectors94II.5Local structure of distribution solutions and of L-closed currents100II.6The approximate Poincare lemma104II.7Approximation and local structure of solutions based on the fine local embedding108II.8Unique continuation of solutions115IIIHypo-Analytic Structures. Hypocomplex Manifolds120III.1Hypo-analytic structures121III.2Properties of hypo-analytic functions128III.3Submanifolds compatible with the hypo-analytic structure130III.4Unique continuation of solutions in a hypo-analytic manifold137III.5Hypocomplex manifolds. Basic properties145III.6Two-dimensional hypocomplex manifolds152Appendix to Section III.6: Some lemmas about first-order differential operators159III.7A class of hypocomplex CR manifolds162IVIntegrable Formal Structures. Normal Forms167IV.1Integrable formal structures168IV.2Hormander numbers, multiplicities, weights. Normal forms174IV.3Lemmas about weights and vector fields178IV.4Existence of basic vector fields of weight - 1185IV.5Existence of normal forms. Pluriharmonic free normal forms. Rigid structures191IV.6Leading parts198VInvolutive Structures with Boundary201V.1Involutive structures with boundary202V.2The associated differential complex. The boundary complex209V.3Locally integrable structures with boundary. The Mayer-Vietoris sequence219V.4Approximation of classical solutions in locally integrable structures with boundary226V.5Distribution solutions in a manifold with totally characteristic boundary228V.6Distribution solutions in a manifold with noncharacteristic boundary235V.7Example: Domains in complex space246VILocal Integrability and Local Solvability in Elliptic Structures252VI.1The Bochner-Martinelli formulas253VI.2Homotopy formulas for [actual symbol not reproducible] in convex and bounded domains258VI.3Estimating the sup norms of the homotopy operators264VI.4Holder estimates for the homotopy operators in concentric balls269VI.5The Newlander-Nirenberg theorem281VI.6End of the proof of the Newlander-Nirenberg theorem287VI.7Local integrability and local solvability of elliptic structures. Levi flat structures291VI.8Partial local group structures297VI.9Involutive structures with transverse group action. Rigid structures. Tube structures303VIIExamples of Nonintegrability and of Nonsolvability312VII.1Mizohata structures314VII.2Nonsolvability and nonintegrability when the signature of the Levi form is |n - 2|319VII.3Mizohata structures on two-dimensional manifolds324VII.4Nonintegrability and nonsolvability when the cotangent structure bundle has rank one330VII.5Nonintegrability and nonsolvability in Lewy structures. The three-dimensional case337VII.6Nonintegrability in Lewy structures. The higher-dimensional case343VII.7Example of a CR structure that is not locally integrable but is locally integrable on one side348VIIINecessary Conditions for the Vanishing of the Cohomology. Local Solvability of a Single Vector Field352VIII.1Preliminary necessary conditions for exactness354VIII.2Exactness of top-degree forms358VIII.3A necessary condition for local exactness based on the Levi form364VIII.4A result about structures whose characteristic set has rank at most equal to one367VIII.5Proof of Theorem VIII.4.1373VIII.6Applications of Theorem VII","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403947483479,"sku":"9780691606705","price":74.8,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691606705.jpg?v=1730484966"},{"product_id":"riemannian-geometry-9780817634902","title":"Riemannian Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003ci\u003eRiemannian Geometry\u003c\/i\u003e is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for first-year graduate students in mathematics and physics.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This is one of the best (if even not just the best) book for those who want to get a good, smooth and quick, but yet thorough introduction to modern Riemannian geometry.\" -Publicationes Mathematicae \"This is a very nice introduction to global Riemannian geometry, which leads the reader quickly to the heart of the topic. Nevertheless, classical results are also discussed on many occasions, and almost 60 pages are devoted to exercises.\" -Newsletter of the EMS \"In the reviewer's opinion, this is a superb book which makes learning a real pleasure.\" -Revue Romaine de Mathematiques Pures et Appliquees \"This mainstream presentation of differential geometry serves well for a course on Riemannian geometry, and it is complemented by many annotated exercises.\" -Monatshefte F. Mathematik\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface to the 1st edition * Preface to the 2nd edition * Preface to the English edition * How to use this book * 0. Differentiable Manifolds * 1. Riemannian Metrics * 2. Affine Connections; Riemannian Connections * 3. Geodesics; Convex Neighborhoods * 4. Curvature * 5. Jacobi Fields * 6. Isometric Immersions * 7. Complete Manifolds; Hopf-Rinow and Hadamard Theorems * 8. Spaces of Constant Curvature * 9. Variations of Energy * 10. The Rauch Comparison Theorem * 11. The Morse Index Theorem * 12. The Fundamental Group of Manifolds of Negative Curvature * 13. The Sphere Theorem * References * Index","brand":"Birkhauser Boston Inc","offers":[{"title":"Default Title","offer_id":49405982835031,"sku":"9780817634902","price":33.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780817634902.jpg?v=1730494135"},{"product_id":"elon-lima-selected-papers-9783030518172","title":"Elon Lima - Selected Papers","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book contains all research papers published by the distinguished Brazilian mathematician Elon Lima. It includes the papers from his PhD thesis on homotopy theory, which are hard to find elsewhere. Elon Lima wrote more than 40 books in the field of topology and dynamical systems. He was a profound mathematician with a genuine vocation to teach and write mathematics.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eComments on some mathematical contributions of Elon Lima.- The Spanier-Whitehead duality in new homotopy categories.- Stable Postnikov invariants and their duals.- Commuting vector fields on 2-manifolds.- On the local triviality of the restriction map for embeddings.- Commuting vector fields on S2.- Common singularities of commuting vector fields on 2-manifolds.- Commuting vector fields on S3.- Isometric immersions with semi-definite second quadratic forms.- Immersions of manifolds with non-negative sectional curvatures.- Orientability of smooth hypersurfaces and the Jordan-Brouwer separation theorem.- The Jordan-Brouwer separation theorem for smooth hypersurfaces. \u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e  \u003cp\u003e\u003cbr\u003e\u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49415622426967,"sku":"9783030518172","price":35.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030518172.jpg?v=1730527549"},{"product_id":"geometric-aspects-of-harmonic-analysis-9783030720575","title":"Geometric Aspects of Harmonic Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis volume originated in talks given in Cortona at the conference \"Geometric aspects of harmonic analysis\" held in honor of the 70th birthday of Fulvio Ricci. It presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest mathematicians working in these areas. The subjects dealt with are topics of current interest in closely interrelated areas of Fourier analysis, singular integral operators, oscillatory integral operators, partial differential equations, multilinear harmonic analysis, and several complex variables.\u003cbr\u003eThe work is addressed to researchers in the field.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e- An Extension Problem and Hardy Type Inequalities for the Grushin Operator. - Sharp Local Smoothing Estimates for Fourier Integral Operators. - On the Hardy–Littlewood Maximal Functions in High Dimensions: Continuous and Discrete Perspective. - Potential Spaces on Lie Groups. - On Fourier Restriction for Finite-Type Perturbations of the Hyperbolic Paraboloid. - On Young’s Convolution Inequality for Heisenberg Groups. - Young’s Inequality Sharpened. - Strongly Singular Integrals on Stratified Groups. - Singular Brascamp–Lieb: A Survey. - On the Restriction of Laplace–Beltrami Eigenfunctions and Cantor-Type Sets. - Basis Properties of the Haar System in Limiting Besov Spaces. - Obstacle Problems Generated by the Estimates of Square Function. - Of Commutators and Jacobians. - On Regularity and Irregularity of Certain Holomorphic Singular Integral Operators.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49415631667543,"sku":"9783030720575","price":127.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030720575.jpg?v=1730527583"},{"product_id":"differential-geometry-of-curves-and-surfaces-9783319397986","title":"Differential Geometry of Curves and Surfaces","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging.\u003cbr\u003eOver 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships.\u003cbr\u003eApplications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut’s Theorem is presented as a conservation law for angular momentum. Green’s Theorem makes possible a drafting tool called a planimeter. Foucault’s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface.\u003cbr\u003eIn truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn’t work without general relativity, formalized through the language of differential geometry. Throughout this book, applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it. \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“This is the first textbook on mathematics that I see printed in color. … This book is not a usual textbook, but a very well written introduction to differential geometry, and the colors really help the reader in understanding the figures and navigating through the text. … this book will surely serve very well for students who want to learn differential geometry from the ground up no matter what their main learning goal is.” (Árpád Kurusa, Acta Scientiarum Mathematicarum, Vol. 84 (1-2), 2018)\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e“This book is perfect for undergraduate students. ... There is also plenty of figures, examples, exercises and applications which make the differential geometry of curves and surfaces so interesting and intuitive. The author uses a rich variety of colours and techniques that help to clarify difficult abstract concepts.” (Teresa Arias-Marco, zbMATH 1375.53001, 2018)\u003c\/p\u003e“This is a visually appealing book, replete with many diagrams, lots of them in full color. … the author’s writing style is extremely clear and well-motivated. … this is still the book I would use as a text for a beginning course on this subject. It would not surprise me if it quickly becomes the market leader.” (Mark Hunacek, MAA Reviews, July, 2017) \u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction.- Curves.- Additional topics in curves.- Surfaces.- The curvature of a surface.- Geodesics.- The Gauss–Bonnet theorem.- Appendix A: The topology of subsets of \u003cb\u003eR\u003c\/b\u003e\u003csup\u003e\u003ci\u003en\u003c\/i\u003e\u003c\/sup\u003e.- Recommended excursions.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49417089089879,"sku":"9783319397986","price":43.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319397986.jpg?v=1730531597"},{"product_id":"differentialgeometrie-von-kurven-und-flachen-9783528072551","title":"Differentialgeometrie von Kurven und Flächen","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eEs gibt in der Differentialgeometrie von Kurven und FJachen zwei Betrachtungsweisen. Die eine, die man klassische Differentialgeometrie nennen konnte, entstand zusammen mit den Anfangen der Differential-und Integralrechnung. Grob gesagt studiert die klassische Differentialgeometrie lokale Eigenschaften von Kurven und FHichen. Dabei verstehen wir unter lokalen Eigenschaften solche, die nur vom Verhalten der Kurve oder Flache in der Umgebung eines Punktes abhiingen. Die Methoden, die sich als fUr das Studium solcher Eigenschaften geeignet erwiesen haben, sind die Methoden der Differentialrechnung. Aus diesem Grund sind die in der Differentialgeometrie untersuchten Kurven und Flachen durch Funktionen definiert, die von einer gewissen Differenzierbarkeitsklasse sind. Die andere Betrachtungsweise ist die sogenannte globale Differentialgeometrie. Hierbei untersucht man den EinfluB lokaler Eigenschaften auf das Verhalten der gesamten Kurve oder Flache. Der interessanteste und reprasentativste Teil der klassischen Differentialgeometrie ist wohl die Untersuchung von Flachen. Beim Studium von Flachen treten jedoch in nattirlicher Weise einige 10k ale Eigenschaften von Kurven auf. Deshalb benutzen wir dieses erste Kapi­ tel, urn kurz auf Kurven einzugehen.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Kurven.- 1.1 Einleitung.- 1.2 Parametrisierte Kurven.- 1.3 Reguläre Kurven. Bogenlänge.- 1.4 Das Vektorprodukt in ?3.- 1.5 Die lokale Theorie von Kurven, die nach der Bogenlänge parametrisiert sind.- 1.6 Die lokale kanonische Form.- 1.7 Globale Eigenschaften ebener Kurven.- 2 Reguläre Flächen.- 2.1 Einleitung.- 2.2 Reguläre Flächen. Urbilder regulärer Werte.- 2.3 Parameterwechsel. Differenzierbare Funktionen auf Flächen.- 2.4 Die Tangentialebene. Das Differential einer Abbildung.- 2.5 Die erste Fundamentalform. Flächeninhalt.- 2.6 Orientierung von Flächen.- 2.7 Eine Charakterisierung kompakter orientierbarer Flächen.- 2.8 Eine geometrische Definition des Flächeninhalts.- 3 Die Geometrie der Gauß-Abbildung.- 3.1 Einleitung.- 3.2 Die Definition der Gauß-Abbildung und ihre fundamentalen Eigenschaften.- 3.3 Die Gauß-Abbildung in lokalen Koordinaten.- 3.4 Vektorfelder.- 3.5 Regelflächen und Minimalflächen.- 4 Die innere Geometrie von Flächen.- 4.1 Einleitung.- 4.2 Isometrie. Konforme Abbildungen.- 4.3 Der Satz von Gauß und die Verträglichkeitsbedingungen.- 4.4 Parallelverschiebung. Geodätische.- 4.5 Der Satz von Gauß-Bonnet und seine Anwendungen.- 4.6 Die Exponentialabbildung. Geodätische Polarkoordinaten.- 4.7 Weitere Eigenschaften von Geodätischen. Konvexe Umgebungen.- Anhang: Beweise der Fundamentalsätze der lokalen Kurven-und Flächentheorie.- Hinweise und Lösungen.- Kommentiertes Literaturverzeichnis.- Namen-und Sachwortverzeichnis.","brand":"Springer Fachmedien Wiesbaden","offers":[{"title":"Default Title","offer_id":49419483185495,"sku":"9783528072551","price":44.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783528072551.jpg?v=1730538482"},{"product_id":"dynamical-systems-vii-integrable-systems-nonholonomic-dynamical-systems-9783642057380","title":"Dynamical Systems VII: Integrable Systems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eA collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eContents: Nonholonomic Dynamical Systems, Geometry of Distributions and Variational Problems by A.M. Vershik, V.Ya. Gershkovich.- Integrable Systems and Infinite Dimensional Lie Algebras by M.A. Olshanetsky, M.A.  Perelomov.- Group-Theoretical Methods in the Theory of Finite-Dimensional Integrable Systems by A.G. Reyman, M.A.  Semenov-Tian-Shansky.- Quantization of Open Toda Lattices by M.A. Semenov-Tian-Shansky.- Geometric and Algebraic Mechanisms of the Integrability of Hamiltonian Systems on Homogeneous Spaces and Lie Algebras by V.V. Trofimov, A.T.  Fomenko.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":49420029165911,"sku":"9783642057380","price":85.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783642057380.jpg?v=1730540529"},{"product_id":"collected-papers-gesammelte-abhandlungen-9783642383687","title":"Collected Papers - Gesammelte Abhandlungen","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eFrom the preface: \"Hopf algebras, Hopf fibration of spheres, Hopf-Rinow complete Riemannian manifolds, Hopf theorem on the ends of groups - can one imagine modern mathematics without all this? Many other concepts and methods, fundamental in various mathematical disciplines, also go back directly or indirectly to the work of Heinz Hopf: homological algebra, singularities of vector fields and characteristic classes, group-like spaces, global differential geometry, and the whole algebraisation of topology with its influence on group theory, analysis and algebraic geometry. It is astonishing to realize that this oeuvre of a whole scientific life consists of only about 70 writings. Astonishing also the transparent and clear style, the concreteness of the problems, and how abstract and far-reaching the methods Hopf invented.\"\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e \u003c\/p\u003e \u003cp\u003eHeinz Hopf (1894-1981) is rightly considered to be one of the outstanding and most influential mathematicians of the XXth century. He was a pioneer in algebraic topology as well as in differential geometry. He is widely known as having studied the ‘Hopf fibration’. The very general abstract notion of Hopf algebra was introduced as tracing in Hopf’s works; he may be considered to have been a forerunner of the creation of homological algebra. He found a noncontractible map of the 3-sphere into the 2-sphere; that result was an essential step towards the concept of ‘Hopf invariant’ and the popularization of the homotopy group notion due to Hurewicz. \u003c\/p\u003e \u003cp\u003eHeinz Hopf was born in Wroclaw (Breslau), in the then German part of Poland. He studied in his home town, in Heidelberg and in Berlin, visited Göttingen, Princeton University, and finally settled at ETH in Zürich, where he became Weyl’s successor.\u003c\/p\u003e \u003cp\u003eThe Heinz Hopf Selecta published in 1964 contained an important – although far from being complete – part of Hopf’s mathematical production. So this volume presenting Hopf’s collected works is welcome. As one may expect, the organisational achievement by Beno Eckmann, Hopf’s student and friend, is high class. Two important articles are translated from German into English.\u003c\/p\u003e \u003cp\u003eThis book of over 1200 pages featuring 71 items constitutes an essential reference for the development of mathematics during the XXth century.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eJean-Paul Pier (Zbl. MATH 980, 01027)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eTable of Contents.- List of Publications of Heinz Hopf.- Editor's Preface.- Papers of Heinz Hopf.- Heinz Hopf Selecta.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":49420036702551,"sku":"9783642383687","price":52.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783642383687.jpg?v=1730540557"},{"product_id":"differentialgeometrie-kurven-flachen-mannigfaltigkeiten-9783658006143","title":"Differentialgeometrie: Kurven - Flächen -","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eDieses Buch ist eine Einführung in die Differentialgeometrie und ein passender Begleiter zum Differentialgeometrie-Modul (ein- und zweisemestrig). Zunächst geht es um die klassischen Aspekte wie die Geometrie von Kurven und Flächen, bevor dann höherdimensionale Flächen sowie abstrakte Mannigfaltigkeiten betrachtet werden. Die Nahtstelle ist dabei das zentrale Kapitel \"Die innere Geometrie von Flächen\". Dieses führt den Leser bis hin zu dem berühmten Satz von Gauß-Bonnet, der ein entscheidendes Bindeglied zwischen lokaler und globaler Geometrie darstellt. Die zweite Hälfte des Buches ist der Riemannschen Geometrie gewidmet. Den Abschluss bildet ein Kapitel über \"Einstein-Räume\", die eine große Bedeutung sowohl in der \"Reinen Mathematik\" als auch in der Allgemeinen Relativitätstheorie von A. Einstein haben. Es wird großer Wert auf Anschaulichkeit gelegt, was durch zahlreiche Abbildungen unterstützt wird.  Bei der Neuauflage wurden einige zusätzliche Lösungen zu den Übungsaufgaben ergänzt.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eBezeichnungen sowie Hilfsmittel aus der Analysis.- Kurven im IRn.- Lokale Flächentheorie, insbes. Drehflächen, Regelflächen, Minimalflächen.- Die innere Geometrie von Flächen.- Riemannsche Mannigfaltigkeiten.- Der Krümmungstensor.- Räume konstanter Krümmung.- Einstein-Räume.- Lösungen zu Übungsaufgaben\u003cbr\u003e.\u003cbr\u003e","brand":"Springer Fachmedien Wiesbaden","offers":[{"title":"Default Title","offer_id":49420112953687,"sku":"9783658006143","price":32.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783658006143.jpg?v=1730540826"},{"product_id":"collected-works-9783662621332","title":"Collected Works","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWhile Eugenio Calabi is best known for his contributions to the theory of Calabi-Yau manifolds, this Steele-Prize-winning geometer’s fundamental contributions to mathematics have been far broader and more diverse than might be guessed from this one aspect of his work. His works have deep influence and lasting impact in global differential geometry, mathematical physics and beyond. By bringing together 47 of Calabi’s important articles in a single volume, this book provides a comprehensive overview of his mathematical oeuvre, and includes papers on complex manifolds, algebraic geometry, Kähler metrics, affine geometry, partial differential equations, several complex variables, group actions and topology. The volume also includes essays on Calabi’s mathematics by several of his mathematical admirers, including S.K. Donaldson, B. Lawson and S.-T. Yau, Marcel Berger; and Jean Pierre Bourguignon. This book is intended  for mathematicians and graduate students around the world. Calabi’s visionary contributions will certainly continue to shape the course of this subject far into the future.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“In my case, I spent several happy hours learning about affine differential geometry, something that would certainly never have happened if I had not picked up this volume. … The collected works of Eugenio Calabi are worthy of a place on the bookshelf of any person with a serious interest in differential geometry.” (Joel Fine, EMS Magazine, May 11, 2023)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface.-  J.-P. Bourguignon, Eugenio Calabi’s Short Biography.- Bibliographic List of Works.- S.-T. Yau, An Essay on Eugenio Calabi.- Part I: Commentaries on Calabi’s Life and Work: B. Lawson, Reflections on the Early Work of Eugenio Calabi.- M. Berger, Encounter with a Geometer: Eugenio Calabi.- J.-P. Bourguignon, Eugenio Calabi and Kähler Metrics.- C. LeBrun, Eugenio Calabi and the Curvature of Kähler Manifolds.- X. Chen, S. Donaldson, Calabi’s Work on Affine Differential Geometry and Results of Bernstein Type.- Part II: Collected Works: E. Calabi ,Ar. Dvoretzky, Convergence- and Sum-Factors for Series of Complex Numbers (1951).- E. Calabi, D. C. Spencer, Completely Integrable Almost Complex Manifolds (1951).- E. Calabi, Metric Riemann Surfaces (1953).- E. Calabi, M. Rosenlicht, Complex Analytic Manifolds Without Countable Base (1953).- E. Calabi, B. Eckmann, A Class of Compact, Complex Manifolds Which Are Not Algebraic (1953).- E. Calabi, Isometric Imbedding of Complex Manifolds (1953).- E. Calabi, The Space of Kähler Metrics (1954).- E. Calabi, The Variation of Kähler Metrics I. The Structure of the Space (1954).- E. Calabi, The Variation of Kähler Metrics II. A Minimum Problem (1954).- E. Calabi, On Kähler Manifolds With Vanishing Canonical Class (1957).- E. Calabi, Construction and Properties of Some 6-Dimensional Almost Complex Manifolds (1958).- E. Calabi, Improper Affine Hyperspheres of Convex Type and a Generalization of a Theorem by K. Jörgens (1958).- E. Calabi, An Extension of E. Hopf’s Maximum Principle with an Application to Riemannian Geometry (1958).- E. Calabi, Errata: An Extension of E. Hopf’s Maximum Principle with an Application to Riemannian Geometry (1959).- E. Calabi, E. Vesentini, Sur les variétés complexes compactes localement symétriques (1959).- E. Calabi, E. Vesentini, On Compact, Locally Symmetric Kähler Manifolds (1960).- E. Calabi, On Compact, Riemannian Manifolds with Constant Curvature I. (1961).- E. Calabi, L. Markus Relativistic Space Forms (1962).- E. Calabi, Linear Systems of Real Quadratic Forms (1964).- E. Calabi, Quasi-Surjective Mappings and a Generalization of Morse Theory (1966).- E. Calabi, Minimal Immersions of Surfaces in Euclidean Spheres (1967).- E. Calabi, On Ricci Curvature and Geodesics (1967).- E. Calabi, On Differentiable Actions of Compact Lie Groups on Compact Manifolds (1968).- E. Calabi, An Intrinsic Characterization of Harmonic One-Forms (1969).- E. Calabi, On the Group of Automorphisms of a Symplectic Manifold (1970).- E. Calabi, P. Hartman, On the Smoothness of Isometries (1970).- E. Calabi, Examples of Bernstein Problems for Some Nonlinear Equations (1970).- E. Calabi, Über singuläre symplektische Strukturen (1971).- E. Calabi, Complete Affine Hyperspheres I (1972).- E. Calabi, A Construction of Nonhomogeneous Einstein Metrics (1975).- E. Calabi, H. S. Wilf, On the Sequential and Random Selection of Subspaces Over a  Finite Field (1977).- E. Calabi, Métriques kählériennes et fibrés  holomorphes (1978).- E. Calabi, Isometric Families of Kähler Structures (1980).- E. Calabi, Géométrie différentielle affine des  hypersurfaces (1981).- E. Calabi, Linear Systems of Real Quadratic Forms II (1982).- E. Calabi, Extremal Kähler Metrics (1982).- E. Calabi, Hypersurfaces with Maximal Affinely Invariant Area (1982).- E. Calabi, Extremal Kähler Metrics II (1985).- E. Calabi, Convex Affine Maximal Surfaces (1988).- E. Calabi, Affine Differential Geometry and Holomorphic Curves (1990).- E. Calabi, J. Cao Simple Closed Geodesics on Convex Surfaces (1992).- F. Beukers, J. A. C. Kolk and E. Calabi, Sums of Generalized Harmonic Series and Volumes (1993).- E. Calabi and H. Gluck, What are the Best Almost-Complex Structures on the 6-Sphere? (1993).- E. Calabi, Extremal Isosystolic Metrics for Compact Surfaces (1996).- E. Calabi, P. J. Olver, A. Tannenbaum, Affine Geometry, Curve Flows, and Invariant Numerical Approximations (1996).- J.-P. Bourguignon, E. Calabi, J. Eells, O. Garcia-Prada, M. Gromov,  Where Does Geometry Go? A Research and Education Perspective (2001).- E. Calabi, X. Chen, The Space of Kähler Metrics II (2002).- Acknowledgements. \u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":49420202869079,"sku":"9783662621332","price":123.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783662621332.jpg?v=1730541146"},{"product_id":"curves-and-surfaces-9788847019409","title":"Curves and Surfaces","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe book provides an introduction to Differential Geometry of Curves and Surfaces. The theory of curves starts with a discussion of possible definitions of the concept of curve, proving in particular the classification of  1-dimensional manifolds. We then present the classical local theory of parametrized plane and space curves (curves in n-dimensional space are discussed in the complementary material): curvature, torsion, Frenet’s formulas and the fundamental  theorem of the local theory of curves. Then, after a self-contained presentation of degree theory for continuous self-maps of the circumference, we study the global theory of plane curves, introducing winding and rotation numbers, and proving the Jordan curve theorem for curves of class C2, and Hopf theorem on the rotation number of closed simple curves. The local theory of surfaces begins with a comparison of the concept of parametrized (i.e., immersed) surface with the concept of regular (i.e., embedded) surface. We then develop the basic differential geometry of surfaces in R3: definitions, examples, differentiable maps and functions, tangent vectors (presented both as vectors tangent to curves in the surface and as derivations on germs of differentiable functions; we shall consistently use both approaches in the whole book) and orientation. Next we study the several notions of curvature on a surface, stressing both the geometrical meaning of the objects introduced and the algebraic\/analytical methods needed to study them via the Gauss map, up to the proof of Gauss’ Teorema Egregium. Then we introduce vector fields on a surface (flow, first integrals, integral curves) and geodesics (definition, basic properties, geodesic curvature, and, in the complementary material, a full proof of minimizing properties of geodesics and of the Hopf-Rinow theorem for surfaces). Then we shall present a proof of the celebrated Gauss-Bonnet theorem, both in its local and in its global form, using basic properties (fully proved in the complementary material) of triangulations of surfaces. As an application, we shall prove the Poincaré-Hopf theorem on zeroes of vector fields.  Finally, the last chapter will be devoted to several important results on the global theory of surfaces, like for instance the characterization of surfaces with constant Gaussian curvature, and the orientability of compact surfaces in R3.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003e“The authors’ goal in writing this book is to present the theory of curves and surfaces from the viewpoint of contemporary mathematics. … New concepts and new definitions are fully motivated, and illustrated by numerous examples. … the book is beautifully written, very well organized, and most of all it may serve as both a less advanced text and a more advanced text for readers interested in the theory of curves and surfaces.” (Andrew Bucki, Mathematical Reviews, June, 2013)\u003c\/p\u003e\u003cp\u003e“It is dedicated to the study of curves and surfaces both from a local and global viewpoint. It is written and organised in such a way that it can be used by a large scope of students, not only for beginning, intermediate or advanced undergraduate courses in mathematics or physics, but also for engineering or computer science students. … the book can be useful for post-graduate students, too. The book is well written and includes many examples and figures.” (Raúl Oset Sinha, Zentralblatt MATH, Vol. 1238, 2012)\u003c\/p\u003e","brand":"Springer Verlag","offers":[{"title":"Default Title","offer_id":49427378078039,"sku":"9788847019409","price":46.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9788847019409.jpg?v=1730564339"},{"product_id":"geometria-differenziale-9788847019195","title":"Geometria Differenziale","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eL'opera fornisce una introduzione alla geometria delle varietà differenziabili, illustrandone le principali proprietà e descrivendo le principali tecniche e i più importanti strumenti usati per il loro studio. Uno degli obiettivi primari dell'opera è di fungere da testo di riferimento per chi (matematici, fisici, ingegneri) usa la geometria differenziale come strumento; inoltre può essere usato come libro di testo per diversi corsi introduttivi alla geometria differenziale, concentrandosi su alcuni dei vari aspetti della teoria presentati nell'opera.  Più in dettaglio, nell'opera saranno trattati i seguenti argomenti: richiami di algebra multilineare e tensoriale, spesso non presentati nei corsi standard di algebra lineare; varietà differenziali, incluso il teorema di Whitney; fibrati vettoriali, incluso il teorema di Frobenius e un'introduzione ai fibrati principali; gruppi di Lie, incluso il teorema di corrispondenza fra sottogruppi e sottoalgebre; coomologia di de Rham, inclusa la dualità di Poincaré e il teorema di de Rham; connessioni, inclusa la teoria delle geodetiche; e geometria Riemanniana, con particolare attenzione agli operatori di curvatura e inclusi teoremi di Cartan-Hadamard, Bonnet-Myers, e Synge-Weinstein. Come abitudine degli autori, il testo è scritto in modo da favorire una lettura attiva, cruciale per un buon apprendimento di argomenti matematici; inoltre è corredato da numerosi esempi svolti ed esercizi proposti.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003e“The book under review is a generous introduction to differential geometry, including basic notions on Lie groups, fiber bundles, cohomology, and an extensive presentation on Riemannian geometry. … This book is a nice introduction to the geometry of differential manifolds: it illustrates the main properties and provides the important instruments. It can be helpful to mathematicians, physicists, engineers, and it can be also used as a textbook for various courses on differential geometry on different levels.” (Cornelia Vizman, Zentralblatt MATH, Vol. 1230, 2012)\u003c\/p\u003e","brand":"Springer Verlag","offers":[{"title":"Default Title","offer_id":49427378110807,"sku":"9788847019195","price":27.54,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9788847019195.jpg?v=1730564339"},{"product_id":"exterior-differential-calculus-and-applications-to-economic-theory-9788876422515","title":"Exterior differential calculus and applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eDuring the academic year 1995\/96, I was invited by the Scuola Normale Superiore to give a series of lectures. The purpose of these notes is to make the underlying economic problems and the mathematical theory of exterior differential systems accessible to a larger number of people. It is the purpose of these notes to go over these results at a more leisurely pace, keeping in mind that mathematicians are not familiar with economic theory and that very few people have read Elie Cartan.","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":49427424346455,"sku":"9788876422515","price":14.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9788876422515.jpg?v=1730564496"},{"product_id":"geometric-properties-of-non-compact-cr-manifolds-9788876423482","title":"Geometric properties of non-compact CR manifolds","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe book deals with some questions related to the boundary problem in complex geometry and CR geometry. After a brief introduction summarizing the main results on the extension of CR functions, it is shown in chapters 2 and 3 that, employing the classical Harvey-Lawson theorem and under suitable conditions, the boundary problem for non-compact maximally complex real submanifolds of C\u003csup\u003en\u003c\/sup\u003e, n=3 is solvable.\u003c\/p\u003e \u003cp\u003eIn chapter 4, the regularity of Levi flat hypersurfaces C\u003csup\u003en\u003c\/sup\u003e (n=3) with assigned boundaries is studied in the graph case, in relation to the existence theorem proved by Dolbeault, Tomassini and Zaitsev. \u003c\/p\u003e \u003cp\u003eFinally, in the last two chapters the structure properties of non-compact Levi-flat submanifolds of C\u003csup\u003en\u003c\/sup\u003e are discussed; in particular, using the theory of the analytic multifunctions, a Liouville theorem for Levi flat submanifolds of C\u003csup\u003en\u003c\/sup\u003e is proved.\u003c\/p\u003e","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":49427425231191,"sku":"9788876423482","price":16.14,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9788876423482.jpg?v=1730564500"},{"product_id":"nevanlinna-theory-9789811067860","title":"Nevanlinna Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book deals with the classical theory of Nevanlinna on the value distribution of meromorphic functions of one complex variable, based on minimum prerequisites for complex manifolds. The theory was extended to several variables by S. Kobayashi, T. Ochiai, J. Carleson, and P. Griffiths in the early 1970s. K. Kodaira took up this subject in his course at The University of Tokyo in 1973 and gave an introductory account of this development in the context of his final paper, contained in this book. The first three chapters are devoted to holomorphic mappings from \u003cb\u003eC\u003c\/b\u003e to complex manifolds. In the fourth chapter, holomorphic mappings between higher dimensional manifolds are covered. The book is a valuable treatise on the Nevanlinna theory, of special interests to those who want to understand Kodaira's unique approach to basic questions on complex manifolds.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface1. Nevanlinna Theory of One Variable (1)1.1 metrics of compact Rimann surfaces1.2 integral formula1.3 holomorphic maps over compact Riemann surfaces whose genus are greater than 21.4 holomorphic maps over Riemann sphreres1.5 Defect relation\u003cbr\u003e2. Schwarz--Kobayashi's Lemma2.1 Schwarz--Kobayashi's Lemma2.2 holomorphic maps over algebraic varieties (general type)2.3 hyperbolic measures\u003cbr\u003e3. Nevanlinna Theory of One Variable (2)3.1 holomorphic maps over Riemann shpres3.2 the first main theorem3.3 the second main theorem\u003cbr\u003e4.  Nevanlinna Theory of Several Variables4.1 Biebelbach's example4.2 the first main theorem4.3 the second main theorem4.4 defect relation4.5 applications\u003cbr\u003eReferences","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":49427818283351,"sku":"9789811067860","price":49.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811067860.jpg?v=1730565781"},{"product_id":"contact-geometry-of-slant-submanifolds-9789811600166","title":"Contact Geometry of Slant Submanifolds","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book contains an up-to-date survey and self-contained chapters on contact slant submanifolds and geometry, authored by internationally renowned researchers. The notion of slant submanifolds was introduced by Prof. B.Y. Chen in 1990, and A. Lotta extended this notion in the framework of contact geometry in 1996. Numerous differential geometers have since obtained interesting results on contact slant submanifolds. \u003cbr\u003eThe book gathers a wide range of topics such as warped product semi-slant submanifolds, slant submersions, semi-slant ξ┴ -, hemi-slant ξ┴ -Riemannian submersions, quasi hemi-slant submanifolds, slant submanifolds of metric f-manifolds, slant lightlike submanifolds, geometric inequalities for slant submanifolds, 3-slant submanifolds, and semi-slant submanifolds of almost paracontact manifolds. The book also includes interesting results on slant curves and magnetic curves, where the latter represents trajectories moving on a Riemannian manifold under the action of magnetic field. It presents detailed information on the most recent advances in the area, making it of much value to scientists, educators and graduate students.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eGeneral Properties of Slant Submanifolds in Contact Metric Manifolds.- Curvature Inequalities for Slant Submanifolds in Pointwise Kenmotsu Space Forms.- Some Basic Inequalities on Slant submanifolds in Space forms.- Geometry of Warped Product Semi-Slant Submanifolds in Almost Contact Metric Manifolds.-  Slant and Semi Slant Submanifolds of Almost Contact and Paracontact Metric Manifolds.- The Slant Submanifolds in the Setting of Metric f-manifolds.- Slant, Semi-Slant and Pointwise Slant Submanifolds of 3-Structure Manifolds.- Slant Submanifolds of Conformal Sasakian Space Forms.- Slant Curves and Magnetic Curves.- Contact Slant Geometry of Submersions and Pointwise Slant and Semi-Slant Warped Product Submanifolds.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":49427822412119,"sku":"9789811600166","price":82.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811600166.jpg?v=1730565795"},{"product_id":"complex-geometry-of-slant-submanifolds-9789811600203","title":"Complex Geometry of Slant Submanifolds","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book contains an up-to-date survey and self-contained chapters on complex slant submanifolds and geometry, authored by internationally renowned researchers. The book discusses a wide range of topics, including slant surfaces, slant submersions, nearly Kaehler, locally conformal Kaehler, and quaternion Kaehler manifolds. It provides several classification results of minimal slant surfaces, quasi-minimal slant surfaces, slant surfaces with parallel mean curvature vector, pseudo-umbilical slant surfaces, and biharmonic and quasi biharmonic slant surfaces in Lorentzian complex space forms. Furthermore, this book includes new results on slant submanifolds of para-Hermitian manifolds. \u003cbr\u003eThis book also includes recent results on slant lightlike submanifolds of indefinite Hermitian manifolds, which are of extensive use in general theory of relativity and potential applications in radiation and electromagnetic fields. Various open problems and conjectures on slant surfaces in complex space forms are also included in the book. It presents detailed information on the most recent advances in the area, making it valuable for scientists, educators and graduate students.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“As a global view, one must mention that many of the presented results in the above contributions are given with their complete proofs; this fact increases the value of the book and makes it excellent scientific material for the researchers in the field. Besides the high level and the valuable contents of the book, one must remark that the topic is of high interest for the specialists in differential geometry.” (Adela-Gabriela Mihai, zbMATH 1511.53002, 2023)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eAn Overview of Recent Developments of Slant Submanifolds.- Slant Surfaces in Complex Space Forms.- Slant Geometry of Warped products in Kaehler and Nearly Kaehler Manifolds.- Slant Geometry of Riemannian Submersions from Almost Hermitian Manifolds.- Slant Submanifolds of the nearly Kaehler 6-sphere.- Slant submanifolds of para Hermitian manifolds.- Hemi-slant and Semi-slant Submanifolds in locally conformal Kaehler Manifolds.- Slant Submanifolds and Their Warped Product in Locally Product Riemannian Manifolds.- Slant Submanifolds of Quaternion Kaehler and Hyper-Kaehler Manifolds.- Geometry of Pointwise Slant Immersions in Almost Hermitian Manifolds.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":49427822543191,"sku":"9789811600203","price":82.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811600203.jpg?v=1730565796"},{"product_id":"einstein-constraints-and-ricci-flow-a-geometrical-averaging-of-initial-data-sets-9789811985393","title":"Einstein Constraints and Ricci Flow: A","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book contains a self-consistent treatment of a geometric averaging technique, induced by the Ricci flow, that allows comparing a given (generalized) Einstein initial data set with another distinct Einstein initial data set, both supported on a given closed \u003ci\u003en\u003c\/i\u003e-dimensional manifold. \u003cbr\u003eThis is a case study where two vibrant areas of research in geometric analysis, Ricci flow and Einstein constraints theory, interact in a quite remarkable way. The interaction is of great relevance for applications in relativistic cosmology, allowing a mathematically rigorous approach to the initial data set averaging problem, at least when data sets are given on a closed space-like hypersurface. \u003cbr\u003eThe book does not assume an a priori knowledge of Ricci flow theory, and considerable space is left for introducing the necessary techniques. These introductory parts gently evolve to a detailed discussion of the more advanced results concerning a Fourier-mode expansion and a sophisticated heat kernel representation of the Ricci flow, both of which are of independent interest in Ricci flow theory. \u003cbr\u003eThis work is intended for advanced students in mathematical physics and researchers alike. \u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction.- Geometric preliminaries.- Ricci flow background.- Ricci flow conjugation of initial data sets.- Concluding remarks.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":49427854819671,"sku":"9789811985393","price":94.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811985393.jpg?v=1730565905"},{"product_id":"lagrangian-floer-theory-and-its-deformations-9789819717972","title":"Lagrangian Floer Theory and Its Deformations","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eBased Loop Space and A8 Space.- A8 Algebras and Modules: Unfiltered Case.- Obstruction-Deformation Theory of Filtered A8 Bimodules.- Symplectic Geometry and Hamiltonian Dynamics.- Analysis of Pseudoholomorphic Curves and Bordered Stable Maps.- Critical Points of Potential Functions and Floer Cohomology.- Filtered Fukaya Category and its Bulk Deformations.\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e","brand":"Springer","offers":[{"title":"Default Title","offer_id":49427871072599,"sku":"9789819717972","price":71.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789819717972.jpg?v=1730565961"},{"product_id":"basic-procedures-in-ordinary-differential-equations-9781684740710","title":"Basic procedures in ordinary differential","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Lulu.com","offers":[{"title":"Default Title","offer_id":49535132402007,"sku":"9781684740710","price":14.81,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781684740710.jpg?v=1731897181"},{"product_id":"matrix-groups-an-introduction-to-lie-group-theory-9781852334703","title":"Matrix Groups: An Introduction to Lie Group","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book offers a first taste of the theory of Lie groups, focusing mainly on matrix groups: closed subgroups of real and complex general linear groups. The first part studies examples and describes classical families of simply connected compact groups. The second section introduces the idea of a lie group and explores the associated notion of a homogeneous space using orbits of smooth actions. The emphasis throughout is on accessibility. \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews of the first edition:\u003c\/p\u003e \u003cp\u003eMATHEMATICAL REVIEWS\u003c\/p\u003e \u003cp\u003e\u003cem\u003e\"This excellent book gives an easy introduction to the theory of Lie groups and Lie algebras by restricting the material to real and complex matrix groups. This provides the reader not only with a wealth of examples, but it also makes the key concepts much more concrete. This combination makes the material in this book more easily accessible for the readers with a limited background…The book is very easy to read and suitable for an elementary course in Lie theory aimed at advanced undergraduates or beginning graduate students…To summarize, this is a well-written book, which is highly suited as an introductory text for beginning graduate students without much background in differential geometry or for advanced undergraduates. It is a welcome addition to the literature in Lie theory.\"\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\"This book is an introduction to Lie group theory with focus on the matrix case. … This book can be recommended to students, making Lie group theory more accessible to them.\" (A. Akutowicz, Zentralblatt MATH, Vol. 1009, 2003)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eI. Basic Ideas and Examples.- 1. Real and Complex Matrix Groups.- 2. Exponentials, Differential Equations and One-parameter Subgroups.- 3. Tangent Spaces and Lie Algebras.- 4. Algebras, Quaternions and Quaternionic Symplectic Groups.- 5. Clifford Algebras and Spinor Groups.- 6. Lorentz Groups.- II. Matrix Groups as Lie Groups.- 7. Lie Groups.- 8. Homogeneous Spaces.- 9. Connectivity of Matrix Groups.- III. Compact Connected Lie Groups and their Classification.- 10. Maximal Tori in Compact Connected Lie Groups.- 11. Semi-simple Factorisation.- 12. Roots Systems, Weyl Groups and Dynkin Diagrams.- Hints and Solutions to Selected Exercises.","brand":"Springer London Ltd","offers":[{"title":"Default Title","offer_id":49535826886999,"sku":"9781852334703","price":29.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781852334703.jpg?v=1731899724"},{"product_id":"global-analysis-9780821829516","title":"Global Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003ePresents an introduction to differential geometry through differential forms, emphasizing their applications in various areas of mathematics and physics. This work focuses on Stokes' theorem, the classical integral formulas and their applications to harmonic functions and topology.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eElements of multilinear algebra Differential forms in ${\\mathbb{R}}^n$ Vector analysis on manifolds Pfaffian systems Curves and surfaces in Euclidean 3-space Lie groups and homogeneous spaces Symplectic geometry and mechanics Elements of statistical mechanics and thermodynamics Elements of electrodynamics Bibliography Symbols Index.","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":49963659788631,"sku":"9780821829516","price":79.2,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780821829516.jpg?v=1739085294"},{"product_id":"differential-geometry-and-lie-groups-a-computational-perspective-9783030460396","title":"Differential Geometry and Lie Groups: A","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook offers an introduction to differential geometry designed for readers interested in modern geometry processing. Working from basic undergraduate prerequisites, the authors develop manifold theory and Lie groups from scratch; fundamental topics in Riemannian geometry follow, culminating in the theory that underpins manifold optimization techniques. Students and professionals working in computer vision, robotics, and machine learning will appreciate this pathway into the mathematical concepts behind many modern applications.\u003cbr\u003e\u003cbr\u003eStarting with the matrix exponential, the text begins with an introduction to Lie groups and group actions. Manifolds, tangent spaces, and cotangent spaces follow; a chapter on the construction of manifolds from gluing data is particularly relevant to the reconstruction of surfaces from 3D meshes. Vector fields and basic point-set topology bridge into the second part of the book, which focuses on Riemannian geometry.\u003cbr\u003e\u003cbr\u003eChapters on Riemannian manifolds encompass Riemannian metrics, geodesics, and curvature. Topics that follow include submersions, curvature on Lie groups, and the Log-Euclidean framework. The final chapter highlights naturally reductive homogeneous manifolds and symmetric spaces, revealing the machinery needed to generalize important optimization techniques to Riemannian manifolds. Exercises are included throughout, along with optional sections that delve into more theoretical topics.\u003cbr\u003e\u003cbr\u003e\u003ci\u003eDifferential Geometry and Lie Groups: A Computational Perspective\u003c\/i\u003e offers a uniquely accessible perspective on differential geometry for those interested in the theory behind modern computing applications. Equally suited to classroom use or independent study, the text will appeal to students and professionals alike; only a background in calculus and linear algebra is assumed. Readers looking to continue on to more advanced topics will appreciate the authors’ companion volume \u003ci\u003eDifferential Geometry and Lie Groups: A Second Course\u003c\/i\u003e.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The book … is intended ‘for a wide audience ranging from upper undergraduate to advanced graduate students in mathematics, physics, and more broadly engineering students, especially in computer science.’ …  The text’s coverage is extensive, its exposition clear throughout, and the color illustrations helpful. The authors are also familiar with many texts at a comparable level and have drawn on them in several places to include some of the most insightful proofs already in the literature.” (Jer-Chin Chuang, MAA Reviews, October 4, 2021)\u003cbr\u003e“The book is intended for incremental study and covers both basic concepts and more advanced ones. The former are thoroughly supported with theory and examples, and the latter are backed up with extensive reading lists and references. … Thanks to its design and approach style this is a timely and much needed addition that enables interdisciplinary bridges and the discovery of new applications for differential geometry.” (Corina Mohorian, zbMATH 1453.53001, 2021)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. The Matrix Exponential; Some Matrix Lie Groups.- 2. Adjoint Representations and the Derivative of exp.- 3. Introduction to Manifolds and Lie Groups.- 4. Groups and Group Actions.- 5. The Lorentz Groups ⊛.- 6. The Structure of O(\u003ci\u003ep\u003c\/i\u003e,\u003ci\u003eq\u003c\/i\u003e) and SO(\u003ci\u003ep\u003c\/i\u003e, \u003ci\u003eq\u003c\/i\u003e).- 7. Manifolds, Tangent Spaces, Cotangent Spaces.- 8. Construction of Manifolds From Gluing Data ⊛.- 9. Vector Fields, Integral Curves, Flows.- 10. Partitions of Unity, Covering Maps ⊛.- 11. Basic Analysis: Review of Series and Derivatives.- 12. A Review of Point Set Topology.-13. Riemannian Metrics, Riemannian Manifolds.- 14. Connections on Manifolds.- 15. Geodesics on Riemannian Manifolds.- 16. Curvature in Riemannian Manifolds.- 17. Isometries, Submersions, Killing Vector Fields.- 18. Lie Groups, Lie Algebra, Exponential Map.- 19. The Derivative of exp and Dynkin's Formula ⊛.- 20. Metrics, Connections, and Curvature of Lie Groups.- 21. The Log-Euclidean Framework.- 22. Manifolds Arising from Group Actions.\u003cp\u003e\u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":50470469402967,"sku":"9783030460396","price":55.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030460396.jpg?v=1744898422"},{"product_id":"geometry-lie-theory-and-applications-the-abel-symposium-2019-9783030812959","title":"Geometry, Lie Theory and Applications: The Abel","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book consists of contributions from the participants of the Abel Symposium 2019 held in Ålesund, Norway. It was centered about applications of the ideas of symmetry and invariance, including equivalence and deformation theory of geometric structures, classification of differential invariants and invariant differential operators, integrability analysis of equations of mathematical physics, progress in parabolic geometry and mathematical aspects of general relativity.\u003cbr\u003eThe chapters are written by leading international researchers, and consist of both survey and research articles. The book gives the reader an insight into the current research in differential geometry and Lie theory, as well as applications of these topics, in particular to general relativity and string theory.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFour-dimensional homogeneous generalizations of Einstein Metrics.- Conformal and isometric embeddings of gravitational instantons.- Recent results on closed G2-structures, by Anna Fino and Alberto Raffero.- Almost Zoll affine surfaces.- Distinguished curves and fist integrals on Poincare-Einstein and other conformally singular geometries.- A car as parabolic geometry.- Legendrian cone structures and contact prolongations.- The search for solitons on homogeneous spaces.- On Ricci negative Lie groups.- Semi-Riemannian cones.- Building new Einstein spaces by deforming symmetric Einstein spaces.- Remarks on highly supersymmetric backgrounds of 11-dimensional supergravity.- Krichever-Novikov type algebras.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":50470471008599,"sku":"9783030812959","price":112.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030812959.jpg?v=1744898429"},{"product_id":"lectures-on-differential-geometry-9789811252648","title":"Lectures On Differential Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book presents a concise introduction to differential geometry. It is aimed at advanced undergraduate students and first year graduate students who wish to have a basic solid knowledge of the subject, and it can serve as a starting point for more advanced reading. The book is organized into lectures, so it can easily be used as a textbook for a beginning graduate-level course in differential geometry.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":50473264578903,"sku":"9789811252648","price":121.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811252648.jpg?v=1744905908"},{"product_id":"riemann-problems-and-jupyter-solutions-9781611976205","title":"Riemann Problems and Jupyter Solutions","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book addresses an important class of mathematical problems (the Riemann problem) for first-order hyperbolic partial differential equations (PDEs), which arise when modeling wave propagation in applications such as fluid dynamics, traffic flow, acoustics, and elasticity.\u003cbr\u003e\u003cbr\u003eIt covers the fundamental ideas related to classical Riemann solutions, including their special structure and the types of waves that arise, as well as the ideas behind fast approximate solvers for the Riemann problem.\u003cbr\u003e\u003cbr\u003eThe emphasis is on the general ideas, but each chapter delves into a particular application. The book is available in electronic form as a collection of Jupyter notebooks that contain executable computer code and interactive figures and animations.","brand":"Society for Industrial \u0026 Applied Mathematics,U.S.","offers":[{"title":"Default Title","offer_id":50578263671127,"sku":"9781611976205","price":51.85,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781611976205.jpg?v=1746098581"},{"product_id":"extrinsic-geometry-of-foliations-9783030700690","title":"Extrinsic Geometry of Foliations","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry. The concept of mixed curvature is central to the discussion, and a version of the deep problem of the Ricci curvature for the case of mixed curvature of foliations is examined. The book is divided into five chapters that deal with integral and variation formulas and curvature and dynamics of foliations. Different approaches and methods (local and global, regular and singular) in solving the problems are described using integral and variation formulas, extrinsic geometric flows, generalizations of the Ricci and scalar curvatures, pseudo-Riemannian and metric-affine geometries, and 'computable' Finsler metrics.\u003c\/p\u003e\u003cp\u003eThe book presents the state of the art in geometric and analytical theory of foliations as a continuation of the authors' life-long work in extrinsic geometry.  It is designed for newcomers to the field as well as experienced geometers working in Riemannian geometry, foliation theory, differential topology, and a wide range of researchers in differential equations and their applications.  It may also be a useful supplement to postgraduate level work and can inspire new interesting topics to explore.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The reader is assumed to have some background in topology and differential geometry. The book is a continuation of the authors’ work in extrinsic geometry and thus provides a useful reference for researchers in this field.” (Emanuel-Ciprian Cismaş, zbMATH 1479.53002, 2022)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- 1. Preliminaries.- 2. Integral formulas.- 3. Prescribing the mean curvature.- 4. Variational formulae.- 5. Extrinsic Geometric flows.- References.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":50578714296663,"sku":"9783030700690","price":66.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030700690.jpg?v=1746100649"},{"product_id":"comparison-finsler-geometry-9783030806521","title":"Comparison Finsler Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis monograph presents recent developments in comparison geometry and geometric analysis on Finsler manifolds. Generalizing the weighted Ricci curvature into the Finsler setting, the author systematically derives the fundamental geometric and analytic inequalities in the Finsler context. Relying only upon knowledge of differentiable manifolds, this treatment offers an accessible entry point to Finsler geometry for readers new to the area.\u003c\/p\u003e  \u003cp\u003eDivided into three parts, the book begins by establishing the fundamentals of Finsler geometry, including Jacobi fields and curvature tensors, variation formulas for arc length, and some classical comparison theorems. Part II goes on to introduce the weighted Ricci curvature, nonlinear Laplacian, and nonlinear heat flow on Finsler manifolds. These tools allow the derivation of the Bochner–Weitzenböck formula and the corresponding Bochner inequality, gradient estimates, Bakry–Ledoux’s Gaussian isoperimetric inequality, and functional inequalities in the Finsler setting. Part III comprises advanced topics: a generalization of the classical Cheeger–Gromoll splitting theorem, the curvature-dimension condition, and the needle decomposition. Throughout, geometric descriptions illuminate the intuition behind the results, while exercises provide opportunities for active engagement.\u003c\/p\u003e  \u003cp\u003e\u003ci\u003eComparison Finsler Geometry\u003c\/i\u003e offers an ideal gateway to the study of Finsler manifolds for graduate students and researchers. Knowledge of differentiable manifold theory is assumed, along with the fundamentals of functional analysis. Familiarity with Riemannian geometry is not required, though readers with a background in the area will find their insights are readily transferrable.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“Finsler geometry is an active area of research in mathematics and has led to numerous real-world applications. This book is a comprehensive introduction to Finsler geometry and its applications. It covers the basic concepts of this geometry. More intuitively, this book provides an accessible introduction to recent developments in comparison geometry and geometric analysis on Finsler manifolds. … this book offers a valuable perspective for those familiar with comparison geometry and geometric analysis.” (Behroz Bidabad, Mathematical Reviews, May, 2023)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eI Foundations of Finsler Geometry.- 1. Warm-up: Norms and inner products.- 2. Finsler manifolds.- 3. Properties of geodesics.- 4. Covariant derivatives.- 5. Curvature.- 6. Examples of Finsler manifolds.- 7. Variation formulas for arclength.- 8. Some comparison theorems.- II Geometry and analysis of weighted Ricci curvature.- 9. Weighted Ricci curvature.- 10. Examples of measured Finsler manifolds.- 11. The nonlinear Laplacian.- 12. The Bochner-Weitzenbock formula.- 13. Nonlinear heat flow.- 14. Gradient estimates.- 15. Bakry-Ledoux isoperimetric inequality.- 16. Functional inequalities.- III Further topics.- 17. Splitting theorems.- 18. Curvature-dimension condition.- 19. Needle decompositions.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":50578714689879,"sku":"9783030806521","price":85.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030806521.jpg?v=1746100649"},{"product_id":"lectures-on-symplectic-geometry-9783540421955","title":"Lectures on Symplectic Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThese notes approximately transcribe a 15-week course on symplectic geometry I taught at UC Berkeley in the Fall of 1997. The course at Berkeley was greatly inspired in content and style by Victor Guillemin, whose masterly teaching of beautiful courses on topics related to s- plectic geometry at MIT, I was lucky enough to experience as a graduate student. I am very thankful to him! That course also borrowed from the 1997 Park City summer courses on symplectic geometry and topology, and from many talks and discussions of the symplectic geometry group at MIT. Among the regular participants in the MIT - formal symplectic seminar 93-96, I would like to acknowledge the contributions of Allen Knutson, Chris Woodward, David Metzler, Eckhard Meinrenken, Elisa Prato, Eugene Lerman, Jonathan Weitsman, Lisa Jeffrey, Reyer Sjamaar, Shaun Martin, Stephanie Singer, Sue Tolman and, last but not least, Yael Karshon. Thanks to everyone sitting in Math 242 in the Fall of 1997 for all the c- ments they made, and especially to those who wrote notes on the basis of which I was better able to reconstruct what went on: Alexandru Scorpan, Ben Davis, David Martinez,DonBarkauskas,EzraMiller,HenriqueBursztyn,John-PeterLund,Laura De Marco, Olga Radko, Peter P? rib' ?k, Pieter Collins, Sarah Packman, Stephen Bigelow, Susan Harrington, Tolga Etgu .. and Yi Ma.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“I find this to be both the best introduction to symplectic geometry as well as a model for how to introduce any field of study. … one feels the hand of a master in the text’s homework sets: concrete, illustrative, and enhancing the material presented. … For an upper-level undergraduate or beginning graduate student, Lectures on Symplectic Geometry remains, in my opinion, an ideal starting point into an exciting, active and growing area of mathematics.” (Andrew McInerney, MAA Reviews, June, 2018)\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eFrom the reviews of the first printing\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eOver the years, there have been several books written to serve as an introduction to symplectic geometry and topology, […] The text under review here fits well within this tradition, providing a useful and effective synopsis of the basics of symplectic geometry and possibly serving as the springboard for a prospective researcher.\u003c\/p\u003e \u003cp\u003eThe material covered here amounts to the \"usual suspects\" of symplectic geometry and topology. From an introductory chapter of symplectic forms and symplectic algebra, the book moves on to many of the subjects that serve as the basis for current research:symplectomorphisms, Lagrangian submanifolds, the Moser theorems, Darboux-Moser-Weinstein theory, almost complex structures, Kãhler structures, Hamiltonian mechanics, symplectic reduction, etc.\u003c\/p\u003e \u003cp\u003eThe text is written in a clear, easy-to-follow style, that is most appropriate in mathematical sophistication for second-year graduate students; […].\u003c\/p\u003e \u003cp\u003eThis text had its origins in a 15-week course that the author taught at UC Berkeley. There are some nice passages where the author simply lists some known results and some well-known conjectures, much as one would expect to see in a good lecture on the same subject. Particularly eloquent is the author’s discussion of the compact examples and counterexamples of symplectic, almost complex, complex and Kähler manifolds.\u003c\/p\u003e \u003cp\u003eThroughout the text, she uses specific, well-chosen examples to illustrate the results. In the initial chapter, she provides a detailed section on the classical example of the syrnplectic structure of the cotangent bundle of a manifold. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eShowing a good sense of pedagogy, the author often leaves these examples as well-planned homework assignments at the end of some of the sections. […] In all of these cases, the author gives the reader a chance to illustrate and understand the interesting results of each section, rather than relegating the tedious but needed results to the reader.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eMathematical Reviews 2002i\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eSymplectic Manifolds.- Symplectic Forms.- Symplectic Form on the Cotangent Bundle.- Symplectomorphisms.- Lagrangian Submanifolds.- Generating Functions.- Recurrence.- Local Forms.- Preparation for the Local Theory.- Moser Theorems.- Darboux-Moser-Weinstein Theory.- Weinstein Tubular Neighborhood Theorem.- Contact Manifolds.- Contact Forms.- Contact Dynamics.- Compatible Almost Complex Structures.- Almost Complex Structures.- Compatible Triples.- Dolbeault Theory.- Kähler Manifolds.- Complex Manifolds.- Kähler Forms.- Compact Kähler Manifolds.- Hamiltonian Mechanics.- Hamiltonian Vector Fields.- Variational Principles.- Legendre Transform.- Moment Maps.- Actions.- Hamiltonian Actions.- Symplectic Reduction.- The Marsden-Weinstein-Meyer Theorem.- Reduction.- Moment Maps Revisited.- Moment Map in Gauge Theory.- Existence and Uniqueness of Moment Maps.- Convexity.- Symplectic Toric Manifolds.- Classification of Symplectic Toric Manifolds.- Delzant Construction.- Duistermaat-Heckman Theorems.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":50579139395927,"sku":"9783540421955","price":49.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783540421955.jpg?v=1746101941"},{"product_id":"a-panoramic-view-of-riemannian-geometry-9783540653172","title":"A Panoramic View of Riemannian Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book introduces readers to the living topics of Riemannian Geometry and details the main results known to date. The results are stated without detailed proofs but the main ideas involved are described, affording the reader a sweeping panoramic view of almost the entirety of the field. \u003c\/p\u003e \u003cp\u003eFrom the reviews \"The book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry.\" --MATHEMATICAL REVIEWS\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\"In this monumental work, Marcel Berger manages to survey large parts of present day Riemannian geometry. … the book offers a great opportunity to get a first impression of some part of Riemannian geometry, together with hints for further reading.\" (A.Cap, Monatshefte für Mathematik, Vol. 145 (4), 2005) \u003c\/p\u003e \u003cp\u003e\"Riemannian geometry has become a vast subject, influencing, famously, the development of general relativity and, more recently, the classification of 3-manifolds by hyperbolic structures … . Marcel Berger’s book is an overview of this enormous subject. … Virtually everything is illustrated with clear and useful diagrams … . This is the sort of book one could dip into or refer to over a period of years.\" (Peter Giblin, The Mathematical Gazette, March, 2005)\u003c\/p\u003e \u003cp\u003e\"Marcel Berger’s A Panoramic View of Riemannian Geometry is without doubt the most comprehensive, original and idiosyncratic treatise on differential geometry … . he manages to include the most up-to-date references on even the most classical topics that he presents, and he puts far greater emphasis on applications. … the book concludes with a massive and extremely useful bibliography of 1310 items.\" (Robert Osserman, SIAM Review, Vol. 47 (1), 2005)\u003c\/p\u003e \u003cp\u003e\"This book of one of the main contributors to Riemannian geometry has as a first goal to give an overview to most of the living topics of the subject. … A second goal is to show how many intuitive geometric questions lead to Riemannian geometry in a natural way. In my opinion it is this way of explaining … which makes the book highly recommendable to students as well as to experienced geometers. Furthermore, this book is clearly an encyclopedia in Riemannian geometry … .\" (F.Manhart, Internationale Mathematische Nachrichten, Issue 197, 2004)\u003c\/p\u003e \u003cp\u003e\"This book is really a panorama. … the reading creates pleasure for the interested reader. … the book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry.\" (Jürgen Eichhorn, Mathematical Reviews, 2004 h)\u003c\/p\u003e \u003cp\u003e\"Riemannian geometry has today become a vast and important subject. This new book of Marcel Berger sets out to introduce readers to most of the living topics of the field and convey them quickly to the main results known to date. … enables the reader to obtain a sweeping panoramic view of almost the entirety of the field.\" (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 49 (3-4), 2003)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e0. Vector fields, tensors 1. Tensor Riemannian duality, the connection and the curvature 2. The parallel transport 3. Absolute (Ricci) calculus, commutation formulas 4. Hodge and the Laplacian, Bochners technique 5. Generalizing Gauss-Bonnet, characteristic classes and C. GEOMETRIC MEASURE THEORY AND PSEUDO-HOLOMORPHIC B. HIGHER DIMENSIONS A.THE CASE OF SURFACES IN R3 C. various other bundles 3. Harmonic maps between Riemannian manifolds 4. Low dimensional Riemannian geometry 5. Some generalizations of Riemannian geometry 6. Gromov mm-spaces 7. Submanifolds B. Spinors A. Exterior differential forms (and some others) C. RICCI FLAT KÄHLER AND HYPERKÄHLER MANIFOLDS 6. Kählerian manifolds (Kähler metrics) Chapter XI : SOME OTHER IMPORTANT TOPICS 1. Non compact manifolds 2. Bundles over Riemannian manifolds B. QUATERNIONIC-KÄHLER MANIFOLDS A. G2 AND Spin(7) HIERRACHY : HOLONOMY GROUPS AND KÄHLER MANIFOLDS 1. Definitions and philosophy 2. Examples 3. General structure theorems 4. The classification result 5. The rare cases b. on a given compact manifolds : closures Chapter X : GLOBAL PARALLEL TRANSPORT AND ANOTHER RIEMANNIAN a. collapsing C. THE CASE OF RICCI CURVATURE 12. Compactness, convergence results 13. The set of all Riemannian structures : collapsing B. MORE FINITENESS THEOREMS A. CHEEGERs FINITENESS THEOREM 11. Finiteness results of all Riemannian structures third part : Finiteness, compactness, collapsing and the space D. NEGATIVE VERSUS NONPOSITIVE CURVATURE 10. The negative side : Ricci curvature C. VOLUMES, FUNDAMENTAL GROUP B. QUASI-ISOMETRIES A. INTRODUCTION E. POSSIBLE APPROACHES, LOOKING FOR THE FUTURE 7. Ricci curvature : positive, nonnegative and just below 8. The positive side : scalar curvature 9. The negative side : sectional curvature D. POSITIVITY OF THE CURVATURE OPERATOR C. THE NON-COMPACT CASE B. HOMOLOGY TYPE AND THE FUNDAMENTAL GROUP A. THE KNOWN EXAMPLES 6. The positive side : sectional curvature second part : Curvature of a given sign1. Introduction 2. The positive pinching 3. Pinching around zero 4. The negative pinching 5. Ricci curvature pinching first part : Pinching problems b. hierarchy of curvaturesa. hopfs urge d. the set of constants, ricci flat metrics 18. The Yamabe problem Chapter IX : from curvature to topology 0. Some history and structure of the chapter c. moduli b. uniqueness a. existence b. homogeneous spaces and others 14. Examples from Analysis I : the evolution Ricci flow 15. Examples from Analysis II : the Kähler case 16. The sporadic examples 17. Around existence and uniqueness a. symmetric spaces THIRD PART : EINSTEIN MANIFOLDS 12. Hilberts variational principle and great hopes 13. The examples from the geometric hierachy 10. The case of Min R d\/2 when d=4 11. Summing up questions on MinVol and Min(R) d\/2 b. the simplicial volume of gromov a. using integral formulas d. cheeger-rong examples 9. Some cases where MinVol \u0026gt; 0 , Min Rd\/2 \u0026gt; 0 c. nilmanifolds and the converse : almost flat manifolds b. wallachs type examples a. s1 fibrations and more examples MinDiam = 0 MinVol, MinDiam 5. Definitions 6. The case of surfaces 7. Generalities, compactness, finiteness and equivalence 8.Cases where MinVol = Min R d\/2 = 0 and SECOND PART : WHICH METRIC IS THE LESS CURVED : Min R d\/2 , FIRST PART: PURE GEOMETRIC FUNCTIONALS 1. Systolic quotients 2. Counting periodic geodesics 3. The embolic volume 4. Diameter\/Injectivity riemannian metric on a given compact manifold ? 0. Introduction and a possible scheme of attack c. the structure on a given Sd and KPn 19. Inverse problems II : conjugacy of geodesics flows Chapter VIII : the search for distinguished metrics : what is the best b. bott and samelson theorems a. definitions and the need to be careful are closed 14. The case of negative curvature 15. The case of nonpositive curvature 16. Entropies on various space forms 17. From Osserman to Lohkamp 18. Inverse problems I : manifolds all of whose geodesics b. the various notions of","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":50579140346199,"sku":"9783540653172","price":104.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783540653172.jpg?v=1746101942"}],"url":"https:\/\/bookcurl.com\/collections\/differential-and-riemannian-geometry.oembed?page=3","provider":"Book Curl","version":"1.0","type":"link"}