{"title":"Differential and Riemannian geometry Books","description":"","products":[{"product_id":"partial-differential-equations-of-mathematical-physics-9780486805153","title":"Partial Differential Equations of Mathematical","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48733806264663,"sku":"9780486805153","price":21.24,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486805153.jpg?v=1791462930"},{"product_id":"the-variational-theory-of-geodesics-dover-books-on-mathematics-9780486838281","title":"The Variational Theory of Geodesics Dover Books","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eCompact, self-contained text by a noted theorist presents essentials of modern differential geometry and basic tools for study of Morse theory. Advanced treatment emphasizes Morse theory's analytical rather than topological aspects. 1967 edition.","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48733830054231,"sku":"9780486838281","price":15.29,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486838281.jpg?v=1791462951"},{"product_id":"an-introduction-to-optimization-on-smooth-manifolds-9781009166171","title":"An Introduction to Optimization on Smooth","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis is a modern invitation to algorithms for optimization with geometry for researchers and advanced undergraduate and graduate students in applied mathematics, computer science and engineering. Readers will appreciate the approachable, yet proof-based, introduction to differential geometry, which is often restricted to pure mathematics curricula.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'With its inviting embedded-first progression and its many examples and exercises, this book constitutes an excellent companion to the literature on Riemannian optimization - from the early developments in the late 20th century to topics that have gained prominence since the 2008 book 'Optimization Algorithms on Matrix Manifolds', and related software, such as Manopt\/Pymanopt\/Manopt.jl.' P.-A. Absil, University of Louvain\u003cbr\u003e'This new book by Nicolas Boumal focuses on optimization on manifolds, which appears naturally in many areas of data science. It successfully covers all important and required concepts in differential geometry with an intuitive and pedagogical approach which is adapted to readers with no prior exposure. Algorithms and analysis are then presented with the perfect mix of significance and mathematical depth. This is a must-read for all graduate students and researchers in data science.' Francis Bach, INRIA\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eNotation; 1. Introduction; 2. Simple examples; 3. Embedded geometry: first order; 4. First-order optimization algorithms; 5. Embedded geometry: second order; 6. Second-order optimization algorithms; 7. Embedded submanifolds: examples; 8. General manifolds; 9. Quotient manifolds; 10. Additional tools; 11. Geodesic convexity; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738007843159,"sku":"9781009166171","price":100.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781009166171.jpg?v=1791468902"},{"product_id":"an-introduction-to-optimization-on-smooth-manifolds-9781009166157","title":"An Introduction to Optimization on Smooth","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis is a modern invitation to algorithms for optimization with geometry for researchers and advanced undergraduate and graduate students in applied mathematics, computer science and engineering. Readers will appreciate the approachable, yet proof-based, introduction to differential geometry, which is often restricted to pure mathematics curricula.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'With its inviting embedded-first progression and its many examples and exercises, this book constitutes an excellent companion to the literature on Riemannian optimization - from the early developments in the late 20th century to topics that have gained prominence since the 2008 book 'Optimization Algorithms on Matrix Manifolds', and related software, such as Manopt\/Pymanopt\/Manopt.jl.' P.-A. Absil, University of Louvain\u003cbr\u003e'This new book by Nicolas Boumal focuses on optimization on manifolds, which appears naturally in many areas of data science. It successfully covers all important and required concepts in differential geometry with an intuitive and pedagogical approach which is adapted to readers with no prior exposure. Algorithms and analysis are then presented with the perfect mix of significance and mathematical depth. This is a must-read for all graduate students and researchers in data science.' Francis Bach, INRIA\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eNotation; 1. Introduction; 2. Simple examples; 3. Embedded geometry: first order; 4. First-order optimization algorithms; 5. Embedded geometry: second order; 6. Second-order optimization algorithms; 7. Embedded submanifolds: examples; 8. General manifolds; 9. Quotient manifolds; 10. Additional tools; 11. Geodesic convexity; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738007941463,"sku":"9781009166157","price":47.26,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781009166157.jpg?v=1723811677"},{"product_id":"differential-geometry-in-the-large-9781108812818","title":"Differential Geometry in the Large","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe 2019 ''Australian-German Workshop on Differential Geometry in the Large'' represented an extraordinary cross section of topics across differential geometry, geometric analysis and differential topology. The two-week programme featured talks from prominent keynote speakers from across the globe, treating geometric evolution equations, structures on manifolds, non-negative curvature and Alexandrov geometry, and topics in differential topology. A joy to the expert and novice alike, this proceedings volume touches on topics as diverse as Ricci and mean curvature flow, geometric invariant theory, Alexandrov spaces, almost formality, prescribed Ricci curvature, and Kähler and Sasaki geometry.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'The high-quality surveys and original work in this book give a convenient path to understand some recent exciting developments in global Differential Geometry and Geometric Analysis. This should be of great value to graduate students entering the field, as well as to more experienced researchers looking for an updated perspective on a wide range of topics, ranging from nonnegative curvature and Alexandrov spaces to geometric flows and equivariant geometry.' Renato G. Bettiol, Lehman College, The City University of New York\u003cbr\u003e'The volume includes important additions to the literature including new results, new proofs of previous results, and simplified expositions, and also an excellent collection of surveys on recent activity. It is well written and offers a generous overview and invitation to a variety of modern, active topics in differential geometry.' Christopher Seaton, MAA Reviews\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction Owen Dearricott, Wilderich Tuschmann, Yuri Nikolayevsky, Thomas Leistner and Diarmuid Crowley; Part I. Geometric Evolution Equations and Curvature Flow: 1. Real geometric invariant theory Christoph Böhm and Ramiro A. Lafuente; 2. Convex ancient solutions to mean curvature flow Theodora Bourni, Mat Langford and Giuseppe Tinaglia; 3. Negatively curved three-manifolds, hyperbolic metrics, isometric embeddings in Minkowski space and the cross curvature flow Paul Bryan, Mohammad N. Ivaki and Julian Scheuer; 4. A mean curvature flow for conformally compact manifolds A. Rod Gover and Valentina-Mira Wheeler; 5. A survey on the Ricci flow on singular spaces Klaus Kröncke and Boris Vertman; Part II. Structures on Manifolds and Mathematical Physics: 6. Some open problems in Sasaki geometry Charles P. Boyer, Hongnian Huang, Eveline Legendre and Christina W. Tønnesen-Friedman; 7. The prescribed Ricci curvature problem for homogeneous metrics Timothy Buttsworth and Artem Pulemotov; 8. Singular Yamabe and Obata problems A. Rod Gover and Andrew K. Waldron; 9. Einstein metrics, harmonic forms and conformally Kähler geometry Claude LeBrun; 10. Construction of the supersymmetric path integral: a survey Matthias Ludewig; 11. Tight models of de-Rham algebras of highly connected manifolds Lorenz Schwachhöfer; Part III. Recent Developments in Non-Negative Sectional Curvature: 12. Fake lens spaces and non-negative sectional curvature Sebastian Goette, Martin Kerin and Krishnan Shankar; 13. Collapsed three-dimensional Alexandrov spaces: a brief survey Fernando Galaz-García, Luis Guijarro and Jesús Núñez-Zimbrón; 14. Pseudo-angle systems and the simplicial Gauss–Bonnet–Chern theorem Stephan Klaus; 15. Aspects and examples on quantitative stratification with lower curvature bounds Nan Li; 16. Universal covers of Ricci limit and RCD spaces Jiayin Pan and Guofang Wei; 17. Local and global homogeneity for manifolds of positive curvature Joseph A. Wolf.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738333917527,"sku":"9781108812818","price":53.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108812818.jpg?v=1791469742"},{"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":57.99,"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":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030284350.jpg?v=1791480468"},{"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":49.49,"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":42.74,"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":49.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319550824.jpg?v=1791379134"},{"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}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319917542.jpg?v=1791379136"},{"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":false}],"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":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783540710493.jpg?v=1791482029"},{"product_id":"poisson-structures-9783642310898","title":"Poisson Structures","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003ePoisson structures appear in a large variety of contexts, ranging from string theory, classical\/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.​\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the book reviews:\u003c\/p\u003e\u003cp\u003e“Each chapter contains a series of exercises as well as a number of notes aimed at giving further hints as to how the various items in the book are interrelated and, furthermore, at placing the material in the literature. … The book is a timely and courageous attempt to make accessible a flourishing research area to a wider audience in the form of a research monograph\/textbook and as such it is very welcome.” (Johannes Huebschmann, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 116, 2014)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e“This book is an excellent presentation of Poisson geometry, its applications and related topics. … This book is suitable for those who have a solid foundation of differential geometry and Lie algebras. The reader will understand why Poisson geometry is such an interesting and important subject.” (Zhuo Chen, zbMATH, Vol. 1284, 2014)\u003c\/p\u003e\u003cp\u003e“This book provides a comprehensive introduction to Poisson structures. … Exercises are given at the end of each chapter … to help readers understand the basic theory. … This is a nice introductory book for both entry level graduate students and advanced researchers who are interested in the subject.” (Xiang Tang, Mathematical Reviews, August, 2013)\u003c\/p\u003e\u003cp\u003e“The book under review deals with very exciting (and current) material presented from a fascinating vantage point and should be welcomed by any scholar whose work touches upon the matters … . its thirteen chapters are peppered with sets of exercises and each chapter comes equipped with supplemental notes that go a bit beyond the text, introduce some historical material, and point to other relevant sources.” (Michael Berg, MAA Reviews, November, 2012)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e​\u003cp\u003ePart I Theoretical Background:1.Poisson Structures: Basic Definitions.- 2.Poisson Structures: Basic Constructions.- 3.Multi-Derivations and Kähler Forms.- 4.Poisson (Co)Homology.- 5.Reduction.- Part II Examples:6.Constant Poisson Structures, Regular and Symplectic Manifolds.- 7.Linear Poisson Structures and Lie Algebras.- 8.Higher Degree Poisson Structures.- 9.Poisson Structures in Dimensions Two and Three.- 10.\u003ci\u003eR\u003c\/i\u003e-Brackets and \u003ci\u003er\u003c\/i\u003e-Brackets.- 11.Poisson–Lie Groups.- Part III Applications:12.Liouville Integrable Systems.- 13.Deformation Quantization.- A Multilinear Algebra.- B Real and Complex Differential Geometry.- References.- Index.- List of Notations.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":48743135019351,"sku":"9783642310898","price":109.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783642310898.jpg?v=1791482051"},{"product_id":"differential-geometry-of-curves-and-surfaces-9789814740241","title":"Differential Geometry Of Curves And Surfaces","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e'In a class populated by students who already have some exposure to the concept of a manifold, the presence of chapter 3 in this text may make for an unusual and interesting course. The primary function of this book will be as a text for a more conventional course in the classical theory of curves and surfaces.'MAA ReviewsThis engrossing volume on curve and surface theories is the result of many years of experience the authors have had with teaching the most essential aspects of this subject. The first half of the text is suitable for a university-level course, without the need for referencing other texts, as it is completely self-contained. More advanced material in the second half of the book, including appendices, also serves more experienced students well.Furthermore, this text is also suitable for a seminar for graduate students, and for self-study. It is written in a robust style that gives the student the opportunity to continue his study at a higher level beyond what a course would usually offer. Further material is included, for example, closed curves, enveloping curves, curves of constant width, the fundamental theorem of surface theory, constant mean curvature surfaces, and existence of curvature line coordinates.Surface theory from the viewpoint of manifolds theory is explained, and encompasses higher level material that is useful for the more advanced student. This includes, but is not limited to, indices of umbilics, properties of cycloids, existence of conformal coordinates, and characterizing conditions for singularities.In summary, this textbook succeeds in elucidating detailed explanations of fundamental material, where the most essential basic notions stand out clearly, but does not shy away from the more advanced topics needed for research in this field. It provides a large collection of mathematically rich supporting topics. Thus, it is an ideal first textbook in this field.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743300890967,"sku":"9789814740241","price":39.9,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789814740241.jpg?v=1791484373"},{"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":63.0,"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":"introduction-to-riemannian-manifolds-9783030801069","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 Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48869361877335,"sku":"9783030801069","price":33.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030801069.jpg?v=1791480537"},{"product_id":"topological-differential-and-conformal-geometry-of-surfaces-9783030890315","title":"Topological, Differential and Conformal Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes’ Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the Gauss–Bonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chow’s Theorem on compact holomorphic submanifolds in complex projective spaces.\u003c\/p\u003e  \u003cp\u003eBased on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e-1. Basic Differential Geometry.- 2. The Geometry of Manifolds.- 3. Hyperbolic Geometry.- 4. Some Examples and Sources of Geometry.- 5. Differential Topology of Surfaces.- 6. Riemann Surfaces.- 7. Surfaces of Genus \u003ci\u003eg\u003c\/i\u003e = 0.- 8. Surfaces with Riemannian Metric.- 9. Outline: Uniformization by Spectral Determinant.- 10. Uniformization by Energy.- 11. Families of Spaces.- 12. Functions on Riemann Surfaces.- 13. Line Bundles and Cohomology.- 14. Moduli Spaces and Teichmüller Spaces.- 15. Dimensions of Spaces of Holomorphic Sections.- 16. The Teichmüller Curve and its Universal Property.- 17. Riemann Surfaces and Algebraic Curves.- 18. The Jacobian of a Riemann Surface.- 19. Special Metrics on \u003ci\u003eJ\u003c\/i\u003e-Surfaces.- 20. The Fundamental Group and Coverings.- A. Reminder: Topology.- References.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48869362139479,"sku":"9783030890315","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030890315.jpg?v=1791480556"},{"product_id":"emerging-topics-on-differential-geometry-graph-theory-9781607410119","title":"Emerging Topics on Differential Geometry \u0026 Graph","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eDifferential geometry is a mathematical discipline that uses the methods of differential and integral calculus to study problems in geometry. Graph theory is also a growing area in mathematical research. In mathematics and computer science, graph theory is the study of mathematical structures used to model pairwise relations between objects from a certain collection. This book presents various theories and applications in both of these mathematical fields. Included are the concepts of dominating sets, one of the most widely studied concepts in graph theory, some current developments of graph theory in the fields of planar linkage mechanisms and geared linkage mechanisms, lie algebras and the application of CR Hamiltonian flows to the deformation theory of CR structures.","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886714892631,"sku":"9781607410119","price":116.24,"currency_code":"GBP","in_stock":false}]},{"product_id":"quantum-mechanics-in-spaces-of-constant-curvature-9781614702719","title":"Quantum Mechanics in Spaces of Constant Curvature","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886850781527,"sku":"9781614702719","price":152.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"geometry-of-curvature-homogeneous-pseudo-riemannian-manifolds-the-9781860947858","title":"Geometry Of Curvature Homogeneous","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003ePseudo-Riemannian geometry is an active research field not only in differential geometry but also in mathematical physics where the higher signature geometries play a role in brane theory. An essential reference tool for research mathematicians and physicists, this book also serves as a useful introduction to students entering this active and rapidly growing field. The author presents a comprehensive treatment of several aspects of pseudo-Riemannian geometry, including the spectral geometry of the curvature tensor, curvature homogeneity, and Stanilov-Tsankov-Videv theory.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eThe Geometry of the Riemann Curvature Tensor; Curvature Homogeneous Generalized Plane Wave Manifolds; Other Pseudo-Riemannian Manifolds; The Curvature Tensor; Complex Osserman Algebraic Curvature Tensors; Stanilov-Tsankov Theory.","brand":"Imperial College Press","offers":[{"title":"Default Title","offer_id":48888196071767,"sku":"9781860947858","price":126.9,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781860947858.jpg?v=1791479103"},{"product_id":"geometry-dynamics-and-foliations-2013-in-honor-of-steven-hurder-and-takashi-tsuboi-on-the-occasion-of-their-60th-birthdays-9784864970402","title":"Geometry, Dynamics, And Foliations 2013: In Honor","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis volume is an outcome of the conference 'Geometry and Foliations 2013' held in Tokyo in September 2013 and associated meetings, aimed for providing a good overview of the present studies as well as some perspective for further studies.The aspects and quality of the volume is represented by B Deroin's survey on Brownian motions on foliated complex surfaces which contains many essential results and ideas.Other articles cover wide topics of foliations and groups of diffeomorphisms old and new; some discuss characteristic classes such as Godbillon-Vey class or homotopy theory of foliations while others deal with topological and differential geometrical aspects, particularly in the holomorphic setting.Also, several articles shows relationship to the geometric group theory.Highly recommended to researchers and graduate students who are interested in and going to study the theories of foliations and related topics such as diffeomorphism groups, geometric group theory.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America","brand":"Mathematical Society of Japan","offers":[{"title":"Default Title","offer_id":48889418809687,"sku":"9784864970402","price":80.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9784864970402.jpg?v=1791482571"},{"product_id":"singularities-in-generic-geometry-9784864970556","title":"Singularities In Generic Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis volume is the proceedings of the workshop 'Singularities in Generic Geometry and Applications — Kobe-Kyoto 2015 (Valencia IV)' — which was held at Kobe University June 3-6 and RIMS, Kyoto University June 8-10, 2015.The workshop was the fourth in a sequence of biennial workshops, which had been started in Valencia (Spain, 2009).The volume consists fifteen original research articles and three survey articles by specialists in Singularity theory and its applications to Differential Topology and Differential Geometry. It is highly recommended to researchers and graduate students who are interested in these areas.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America","brand":"Mathematical Society of Japan","offers":[{"title":"Default Title","offer_id":48889418940759,"sku":"9784864970556","price":85.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9784864970556.jpg?v=1791482572"},{"product_id":"algebraic-geometry-in-east-asia-hanoi-2005-9784931469457","title":"Algebraic Geometry In East Asia -- Hanoi 2005","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis volume is the outcome of the conference “Algebraic Geometry in East Asia. II” which was held at the Conference Hall (Hanoi, Vietnam) during October 10 - October 14, 2005. It collects two survey articles and eight research articles contributed by the invited lecturers. Topics touched upon in this volume include: Zariski pairs, rational homogeneous manifolds, Kummer surfaces, singularity theory, Cremona groups, algebraic curves, dual varieties, Castelnuovo-Weil lattices and so on. The reader can not only find the current status of a variety of research topics but also enjoy the art of the subjects by leading algebraic geometers.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eA survey on Zariski pairs by E. A. Bartolo, J. I. Cogolludo, and H. Tokunaga Towards a categorical construction of Lie algebras by K. Saito Elliptic parameters and defining equations for elliptic fibrations on a Kummer surface by M. Kuwata and T. Shioda Characterization of the rational homogeneous space associated to a long simple root by its variety of minimal rational tangents by J. Hong and J.-M. Hwang Maximal divisorial sets in arc spaces by S. Ishii Two non-conjugate embeddings of $S_3\\times \\mathbb{Z}_2$ into the Cremona group II by V. A. Iskovskikh On the Castelnuovo-Severi inequality for a double covering by C. Keem and A. Ohbuchi Poincare polynomial of a class of signed complete graphic arrangements by G. Jiang, J. Yu, and J. Zhang Singularities of dual varieties in characteristic 2 by I. Shimada On the Castelnuovo-Weil lattices, I by V. Nguyen-Khac and T. Shioda.","brand":"Mathematical Society of Japan","offers":[{"title":"Default Title","offer_id":48889420185943,"sku":"9784931469457","price":41.8,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9784931469457.jpg?v=1791482576"},{"product_id":"finsler-geometry-sapporo-2005-in-memory-of-makoto-matsumoto-9784931469426","title":"Finsler Geometry, Sapporo 2005 -- In Memory Of","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe volume contains surveys and original articles based on the talks given at the 40-th Finsler Symposium on Finsler Geometry held in the period September 9-10, 2005 at Hokkaido Tokai University, Sapporo, Japan. The Symposium's purpose was not only a meeting of the Finsler geometers from Japan and abroad, but also to commemorate the memory of the late Professor Makoto Matsumoto. The papers included in this volume contain fundamental topics of modern Riemann-Finsler geometry, interesting not only for specialists in Finsler geometry, but for researchers in Riemannian geometry or other fields of differential geometry and its applications also.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePart I. Professor Makoto Matsumoto: Photos of Makoto Matsumoto Matsumoto's legacy. The life and work of Professor Makoto Matsumoto by H. Shimada and S. V. Sabau Part II. Hunting Unicorns and Other Topics of Global Finsler Geometry: On two curvature-driven problems in Riemann-Finsler geometry by D. Bao Curvature properties of $(\\alpha, \\beta)$-metrics by S. Bacso, X. Cheng, and Z. Shen A connectedness principle in positively curved Finsler manifolds by I. R. Peter Riemann-Finsler surfaces by S. V. Sabau and H. Shimada Finsler geometry in the tangent bundle by L. Tamassy Part III. Finslerian Inspired Differential Geometry: Perturbations of constant connection Wagner spaces by P. L. Antonelli and S. F. Rutz Path geometries and almost Grassmann structures by M. Crampin and D. J. Saunders Ehresmann connections, metrics and good metric derivatives by R. L. Lovas, J. Pek, and J. Szilasi Dynamical systems of the Lagrangian and Hamiltonian mechanical systems by R. Miron Part IV. Complex Finsler Geometry: The Chern-Finsler connection and Finsler-Kahler manifolds by T. Aikou A survey of complex Finsler geometry by P.-M. Wong.","brand":"Mathematical Society of Japan","offers":[{"title":"Default Title","offer_id":48889420317015,"sku":"9784931469426","price":56.05,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9784931469426.jpg?v=1791482576"},{"product_id":"differential-geometry-for-physicists-9789810231057","title":"Differential Geometry For Physicists","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book is divided into fourteen chapters, with 18 appendices as introduction to prerequisite topological and algebraic knowledge, etc. The first seven chapters focus on local analysis. This part can be used as a fundamental textbook for graduate students of theoretical physics. Chapters 8-10 discuss geometry on fibre bundles, which facilitates further reference for researchers. 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It consists of two parts: the first part contains an introduction to the geometric theory of characteristic classes due to Shiing-shen Chern and André Weil, as well as a proof of the Gauss-Bonnet-Chern theorem based on the Mathai-Quillen construction of Thom forms; the second part presents analytic proofs of the Poincaré-Hopf index formula, as well as the Morse inequalities based on deformations introduced by Edward Witten.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eChern-Weil theory for characteristic classes; Bott and Duistermaat-Heckman formulas; Gauss-Bonnet-Chern theorem; Poincar -Hopf index formula - an analytic proof; morse inequalities - an analytic proof; Thom-Smale and Witten complexes; Atiyah theorem on Kervaire Semi-characteristic.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48890171195735,"sku":"9789810246860","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789810246860.jpg?v=1722557784"},{"product_id":"minimal-submanifolds-and-related-topics-9789812386878","title":"Minimal Submanifolds And Related Topics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe Bernstein problem and the Plateau problem are central topics in the theory of minimal submanifolds. 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Finally, the authors point out the close connection of the subject with some areas of physics.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48890198098263,"sku":"9789812388964","price":106.4,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789812388964.jpg?v=1791484018"},{"product_id":"applied-differential-geometry-a-modern-introduction-9789812706140","title":"Applied Differential Geometry: A Modern","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the world's leading human motion simulator — “Human Biodynamics Engine”, a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools — this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. 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The book applies known results to describe various geometries and their invariants, and presents problems concerned with linear algebra, such as in real and complex analysis, differential equations, differentiable manifolds, differential geometry, Markov chains and transformation groups. 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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":39.99,"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. 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Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eNew features of this revised and expanded second edition include:\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cul\u003e\n\u003cli\u003e\n\u003cp\u003e \u003c\/p\u003ea chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book.  \u003cp\u003e\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\n\u003c\/li\u003e\n\u003cli\u003eCoverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature.\u003c\/li\u003e\n\u003c\/ul\u003e\u003cul\u003e\n\u003cli\u003eAround 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com\u003c\/li\u003e\n\u003cli\u003eul\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e. 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Curating the content carefully, the author builds to a proof of the spectral theorem in the early part of the book. Subsequent chapters illustrate a variety of application areas, exploring key examples in detail. Readers looking to delve further into specialized topics will find ample references to classic and recent literature.\u003c\/p\u003e  Beginning with a brief introduction to functional analysis, the text focuses on unbounded operators and separable Hilbert spaces as the essential tools needed for the subsequent theory. A thorough discussion of the concepts of spectrum and resolvent follows, leading to a complete proof of the spectral theorem for unbounded self-adjoint operators. Applications of spectral theory to differential operators comprise the remaining four chapters. 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Background Material.- References.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49084750135639,"sku":"9783030380014","price":49.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030380014.jpg?v=1791480478"},{"product_id":"differential-geometry-9783031623837","title":"Differential Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49084761014615,"sku":"9783031623837","price":40.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031623837.jpg?v=1791480735"},{"product_id":"calculo-diferencial-9780244694272","title":"Calculo Diferencial","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Lulu.com","offers":[{"title":"Default Title","offer_id":49400414667095,"sku":"9780244694272","price":134.9,"currency_code":"GBP","in_stock":true}]},{"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":98.1,"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":37.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780817634902.jpg?v=1730494135"},{"product_id":"introduction-to-differential-geometry-with-tensor-applications-9781119795629","title":"Introduction to Differential Geometry with Tensor","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eINTRODUCTION TO DIFFERENTIAL GEOMETRY WITH TENSOR APPLICATIONS  This is the only volume of its kind to explain, in precise and easy-to-understand language, the fundamentals of tensors and their applications in differential geometry and analytical mechanics with examples for practical applications and questions for use in a course setting. Introduction to Differential Geometry with Tensor Applications discusses the theory of tensors, curves and surfaces and their applications in Newtonian mechanics. Since tensor analysis deals with entities and properties that are independent of the choice of reference frames, it forms an ideal tool for the study of differential geometry and also of classical and celestial mechanics. This book provides a profound introduction to the basic theory of differential geometry: curves and surfaces and analytical mechanics with tensor applications. The author has tried to keep the treatment of the advanced material as lucid and comprehensive as possible, mainly\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003eAbout the Book xvii\u003c\/p\u003e \u003cp\u003eIntroduction 1\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I: Tensor Theory 7\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Preliminaries 9\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 9\u003c\/p\u003e \u003cp\u003e1.2 Systems of Different Orders 9\u003c\/p\u003e \u003cp\u003e1.3 Summation Convention Certain Index 10\u003c\/p\u003e \u003cp\u003e1.3.1 Dummy Index 11\u003c\/p\u003e \u003cp\u003e1.3.2 Free Index 11\u003c\/p\u003e \u003cp\u003e1.4 Kronecker Symbols 11\u003c\/p\u003e \u003cp\u003e1.5 Linear Equations 14\u003c\/p\u003e \u003cp\u003e1.6 Results on Matrices and Determinants of Systems 15\u003c\/p\u003e \u003cp\u003e1.7 Differentiation of a Determinant 18\u003c\/p\u003e \u003cp\u003e1.8 Examples 19\u003c\/p\u003e \u003cp\u003e1.9 Exercises 23\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Tensor Algebra 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 25\u003c\/p\u003e \u003cp\u003e2.2 Scope of Tensor Analysis 25\u003c\/p\u003e \u003cp\u003e2.2.1 n-Dimensional Space 26\u003c\/p\u003e \u003cp\u003e2.3 Transformation of Coordinates in S n 27\u003c\/p\u003e \u003cp\u003e2.3.1 Properties of Admissible Transformation of Coordinates 30\u003c\/p\u003e \u003cp\u003e2.4 Transformation by Invariance 31\u003c\/p\u003e \u003cp\u003e2.5 Transformation by Covariant Tensor and Contravariant Tensor 32\u003c\/p\u003e \u003cp\u003e2.6 The Tensor Concept: Contravariant and Covariant Tensors 34\u003c\/p\u003e \u003cp\u003e2.6.1 Covariant Tensors 34\u003c\/p\u003e \u003cp\u003e2.6.2 Contravariant Vectors 35\u003c\/p\u003e \u003cp\u003e2.6.3 Tensor of Higher Order 40\u003c\/p\u003e \u003cp\u003e2.6.3.1 Contravariant Tensors of Order Two 40\u003c\/p\u003e \u003cp\u003e2.6.3.2 Covariant Tensor of Order Two 41\u003c\/p\u003e \u003cp\u003e2.6.3.3 Mixed Tensors of Order Two 42\u003c\/p\u003e \u003cp\u003e2.7 Algebra of Tensors 43\u003c\/p\u003e \u003cp\u003e2.7.1 Equality of Two Tensors of Same Type 45\u003c\/p\u003e \u003cp\u003e2.8 Symmetric and Skew-Symmetric Tensors 45\u003c\/p\u003e \u003cp\u003e2.8.1 Symmetric Tensors 45\u003c\/p\u003e \u003cp\u003e2.8.2 Skew-Symmetric Tensors 46\u003c\/p\u003e \u003cp\u003e2.9 Outer Multiplication and Contraction 51\u003c\/p\u003e \u003cp\u003e2.9.1 Outer Multiplication 51\u003c\/p\u003e \u003cp\u003e2.9.2 Contraction of a Tensor 53\u003c\/p\u003e \u003cp\u003e2.9.3 Inner Product of Two Tensors 54\u003c\/p\u003e \u003cp\u003e2.10 Quotient Law of Tensors 56\u003c\/p\u003e \u003cp\u003e2.11 Reciprocal Tensor of a Tensor 58\u003c\/p\u003e \u003cp\u003e2.12 Relative Tensor, Cartesian Tensor, Affine Tensor, and Isotropic Tensors 60\u003c\/p\u003e \u003cp\u003e2.12.1 Relative Tensors 60\u003c\/p\u003e \u003cp\u003e2.12.2 Cartesian Tensors 63\u003c\/p\u003e \u003cp\u003e2.12.3 Affine Tensors 63\u003c\/p\u003e \u003cp\u003e2.12.4 Isotropic Tensor 64\u003c\/p\u003e \u003cp\u003e2.12.5 Pseudo-Tensors 64\u003c\/p\u003e \u003cp\u003e2.13 Examples 65\u003c\/p\u003e \u003cp\u003e2.14 Exercises 71\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Riemannian Metric 73\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 73\u003c\/p\u003e \u003cp\u003e3.2 The Metric Tensor 74\u003c\/p\u003e \u003cp\u003e3.3 Conjugate Tensor 75\u003c\/p\u003e \u003cp\u003e3.4 Associated Tensors 77\u003c\/p\u003e \u003cp\u003e3.5 Length of a Vector 84\u003c\/p\u003e \u003cp\u003e3.5.1 Length of Vector 84\u003c\/p\u003e \u003cp\u003e3.5.2 Unit Vector 85\u003c\/p\u003e \u003cp\u003e3.5.3 Null Vector 86\u003c\/p\u003e \u003cp\u003e3.6 Angle Between Two Vectors 86\u003c\/p\u003e \u003cp\u003e3.6.1 Orthogonality of Two Vectors 87\u003c\/p\u003e \u003cp\u003e3.7 Hypersurface 88\u003c\/p\u003e \u003cp\u003e3.8 Angle Between Two Coordinate Hypersurfaces 89\u003c\/p\u003e \u003cp\u003e3.9 Exercises 95\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Tensor Calculus 97\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 97\u003c\/p\u003e \u003cp\u003e4.2 Christoffel Symbols 97\u003c\/p\u003e \u003cp\u003e4.2.1 Properties of Christoffel Symbols 98\u003c\/p\u003e \u003cp\u003e4.3 Transformation of Christoffel Symbols 110\u003c\/p\u003e \u003cp\u003e4.3.1 Law of Transformation of Christoffel Symbols of 1st Kind 110\u003c\/p\u003e \u003cp\u003e4.3.2 Law of Transformation of Christoffel Symbols of 2nd Kind 111\u003c\/p\u003e \u003cp\u003e4.4 Covariant Differentiation of Tensor 113\u003c\/p\u003e \u003cp\u003e4.4.1 Covariant Derivative of Covariant Tensor 114\u003c\/p\u003e \u003cp\u003e4.4.2 Covariant Derivative of Contravariant Tensor 115\u003c\/p\u003e \u003cp\u003e4.4.3 Covariant Derivative of Tensors of Type (0,2) 116\u003c\/p\u003e \u003cp\u003e4.4.4 Covariant Derivative of Tensors of Type (2,0) 118\u003c\/p\u003e \u003cp\u003e4.4.5 Covariant Derivative of Mixed Tensor of Type (s, r) 120\u003c\/p\u003e \u003cp\u003e4.4.6 Covariant Derivatives of Fundamental Tensors and the Kronecker Delta 120\u003c\/p\u003e \u003cp\u003e4.4.7 Formulas for Covariant Differentiation 122\u003c\/p\u003e \u003cp\u003e4.4.8 Covariant Differentiation of Relative Tensors 123\u003c\/p\u003e \u003cp\u003e4.5 Gradient, Divergence, and Curl 129\u003c\/p\u003e \u003cp\u003e4.5.1 Gradient 130\u003c\/p\u003e \u003cp\u003e4.5.2 Divergence 130\u003c\/p\u003e \u003cp\u003e4.5.2.1 Divergence of a Mixed Tensor (1,1) 132\u003c\/p\u003e \u003cp\u003e4.5.3 Laplacian of an Invariant 136\u003c\/p\u003e \u003cp\u003e4.5.4 Curl of a Covariant Vector 137\u003c\/p\u003e \u003cp\u003e4.6 Exercises 141\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Riemannian Geometry 143\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 143\u003c\/p\u003e \u003cp\u003e5.2 Riemannian-Christoffel Tensor 143\u003c\/p\u003e \u003cp\u003e5.3 Properties of Riemann-Christoffel Tensors 150\u003c\/p\u003e \u003cp\u003e5.3.1 Space of Constant Curvature 158\u003c\/p\u003e \u003cp\u003e5.4 Ricci Tensor, Bianchi Identities, Einstein Tensors 159\u003c\/p\u003e \u003cp\u003e5.4.1 Ricci Tensor 159\u003c\/p\u003e \u003cp\u003e5.4.2 Bianchi Identity 160\u003c\/p\u003e \u003cp\u003e5.4.3 Einstein Tensor 166\u003c\/p\u003e \u003cp\u003e5.5 Einstein Space 170\u003c\/p\u003e \u003cp\u003e5.6 Riemannian and Euclidean Spaces 171\u003c\/p\u003e \u003cp\u003e5.6.1 Riemannian Spaces 171\u003c\/p\u003e \u003cp\u003e5.6.2 Euclidean Spaces 174\u003c\/p\u003e \u003cp\u003e5.7 Exercises 175\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 The e-Systems and the Generalized Kronecker Deltas 177\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 177\u003c\/p\u003e \u003cp\u003e6.2 e-Systems 177\u003c\/p\u003e \u003cp\u003e6.3 Generalized Kronecker Delta 181\u003c\/p\u003e \u003cp\u003e6.4 Contraction of δ\u003csup\u003eijk\u003c\/sup\u003e \u003csub\u003eαβγ\u003c\/sub\u003e 183\u003c\/p\u003e \u003cp\u003e6.5 Application of e-Systems to Determinants and Tensor Characters of Generalized Kronecker Deltas 185\u003c\/p\u003e \u003cp\u003e6.5.1 Curl of Covariant Vector 189\u003c\/p\u003e \u003cp\u003e6.5.2 Vector Product of Two Covariant Vectors 190\u003c\/p\u003e \u003cp\u003e6.6 Exercises 192\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II: Differential Geometry 193\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Curvilinear Coordinates in Space 195\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 195\u003c\/p\u003e \u003cp\u003e7.2 Length of Arc 195\u003c\/p\u003e \u003cp\u003e7.3 Curvilinear Coordinates in E 3 200\u003c\/p\u003e \u003cp\u003e7.3.1 Coordinate Surfaces 201\u003c\/p\u003e \u003cp\u003e7.3.2 Coordinate Curves 202\u003c\/p\u003e \u003cp\u003e7.3.3 Line Element 205\u003c\/p\u003e \u003cp\u003e7.3.4 Length of a Vector 206\u003c\/p\u003e \u003cp\u003e7.3.5 Angle Between Two Vectors 207\u003c\/p\u003e \u003cp\u003e7.4 Reciprocal Base Systems 210\u003c\/p\u003e \u003cp\u003e7.5 Partial Derivative 216\u003c\/p\u003e \u003cp\u003e7.6 Exercises 219\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Curves in Space 221\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 221\u003c\/p\u003e \u003cp\u003e8.2 Intrinsic Differentiation 221\u003c\/p\u003e \u003cp\u003e8.3 Parallel Vector Fields 226\u003c\/p\u003e \u003cp\u003e8.4 Geometry of Space Curves 228\u003c\/p\u003e \u003cp\u003e8.4.1 Plane 231\u003c\/p\u003e \u003cp\u003e8.5 Serret-Frenet Formula 233\u003c\/p\u003e \u003cp\u003e8.5.1 Bertrand Curves 235\u003c\/p\u003e \u003cp\u003e8.6 Equations of a Straight Line 252\u003c\/p\u003e \u003cp\u003e8.7 Helix 254\u003c\/p\u003e \u003cp\u003e8.7.1 Cylindrical Helix 256\u003c\/p\u003e \u003cp\u003e8.7.2 Circular Helix 258\u003c\/p\u003e \u003cp\u003e8.8 Exercises 262\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Intrinsic Geometry of Surfaces 265\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 265\u003c\/p\u003e \u003cp\u003e9.2 Curvilinear Coordinates on a Surface 265\u003c\/p\u003e \u003cp\u003e9.3 Intrinsic Geometry: First Fundamental Quadratic Form 267\u003c\/p\u003e \u003cp\u003e9.3.1 Contravariant Metric Tensor 270\u003c\/p\u003e \u003cp\u003e9.4 Angle Between Two Intersecting Curves on a Surface 272\u003c\/p\u003e \u003cp\u003e9.4.1 Pictorial Interpretation 274\u003c\/p\u003e \u003cp\u003e9.5 Geodesic in R n 277\u003c\/p\u003e \u003cp\u003e9.6 Geodesic Coordinates 289\u003c\/p\u003e \u003cp\u003e9.7 Parallel Vectors on a Surface 291\u003c\/p\u003e \u003cp\u003e9.8 Isometric Surface 292\u003c\/p\u003e \u003cp\u003e9.8.1 Developable 293\u003c\/p\u003e \u003cp\u003e9.9 The Riemannian–Christoffel Tensor and Gaussian Curvature 294\u003c\/p\u003e \u003cp\u003e9.9.1 Einstein Curvature 296\u003c\/p\u003e \u003cp\u003e9.10 The Geodesic Curvature 308\u003c\/p\u003e \u003cp\u003e9.11 Exercises 319\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Surfaces in Space 321\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 321\u003c\/p\u003e \u003cp\u003e10.2 The Tangent Vector 321\u003c\/p\u003e \u003cp\u003e10.3 The Normal Line to the Surface 324\u003c\/p\u003e \u003cp\u003e10.4 Tensor Derivatives 329\u003c\/p\u003e \u003cp\u003e10.5 Second Fundamental Form of a Surface 332\u003c\/p\u003e \u003cp\u003e10.5.1 Equivalence of Definition of Tensor b αβ 333\u003c\/p\u003e \u003cp\u003e10.6 The Integrability Condition 334\u003c\/p\u003e \u003cp\u003e10.7 Formulas of Weingarten 337\u003c\/p\u003e \u003cp\u003e10.7.1 Third Fundamental Form 338\u003c\/p\u003e \u003cp\u003e10.8 Equations of Gauss and Codazzi 339\u003c\/p\u003e \u003cp\u003e10.9 Mean and Total Curvatures of a Surface 341\u003c\/p\u003e \u003cp\u003e10.10 Exercises 347\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Curves on a Surface 349\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 349\u003c\/p\u003e \u003cp\u003e11.2 Curve on a Surface: Theorem of Meusnier 350\u003c\/p\u003e \u003cp\u003e11.2.1 Theorem of Meusnier 353\u003c\/p\u003e \u003cp\u003e11.3 The Principal Curvatures of a Surface 358\u003c\/p\u003e \u003cp\u003e11.3.1 Umbillic Point 360\u003c\/p\u003e \u003cp\u003e11.3.2 Lines of Curvature 361\u003c\/p\u003e \u003cp\u003e11.3.3 Asymptotic Lines 362\u003c\/p\u003e \u003cp\u003e11.4 Rodrigue’s Formula 376\u003c\/p\u003e \u003cp\u003e11.5 Exercises 379\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Curvature of Surface 381\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 381\u003c\/p\u003e \u003cp\u003e12.2 Surface of Positive and Negative Curvatures 381\u003c\/p\u003e \u003cp\u003e12.3 Parallel Surfaces 383\u003c\/p\u003e \u003cp\u003e12.3.1 Computation of aαβ and b αβ 383\u003c\/p\u003e \u003cp\u003e12.4 The Gauss-Bonnet Theorem 387\u003c\/p\u003e \u003cp\u003e12.5 The n-Dimensional Manifolds 391\u003c\/p\u003e \u003cp\u003e12.6 Hypersurfaces 394\u003c\/p\u003e \u003cp\u003e12.7 Exercises 395\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III: Analytical Mechanics 397\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Classical Mechanics 399\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 399\u003c\/p\u003e \u003cp\u003e13.2 Newtonian Laws of Motion 399\u003c\/p\u003e \u003cp\u003e13.3 Equations of Motion of Particles 401\u003c\/p\u003e \u003cp\u003e13.4 Conservative Force Field 403\u003c\/p\u003e \u003cp\u003e13.5 Lagrangean Equations of Motion 405\u003c\/p\u003e \u003cp\u003e13.6 Applications of Lagrangean Equations 411\u003c\/p\u003e \u003cp\u003e13.7 Himilton’s Principle 423\u003c\/p\u003e \u003cp\u003e13.8 Principle of Least Action 427\u003c\/p\u003e \u003cp\u003e13.9 Generalized Coordinates 430\u003c\/p\u003e \u003cp\u003e13.10 Lagrangean Equations in Generalized Coordinates 432\u003c\/p\u003e \u003cp\u003e13.11 Divergence Theorem, Green’s Theorem, Laplacian Operator, and Stoke’s Theorem in Tensor Notation 438\u003c\/p\u003e \u003cp\u003e13.12 Hamilton’s Canonical Equations 442\u003c\/p\u003e \u003cp\u003e13.12.1 Generalized Momenta 443\u003c\/p\u003e \u003cp\u003e13.13 Exercises 444\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Newtonian Law of Gravitations 447\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 447\u003c\/p\u003e \u003cp\u003e14.2 Newtonian Laws of Gravitation 447\u003c\/p\u003e \u003cp\u003e14.3 Theorem of Gauss 451\u003c\/p\u003e \u003cp\u003e14.4 Poisson’s Equation 453\u003c\/p\u003e \u003cp\u003e14.5 Solution of Poisson’s Equation 454\u003c\/p\u003e \u003cp\u003e14.6 The Problem of Two Bodies 456\u003c\/p\u003e \u003cp\u003e14.7 The Problem of Three Bodies 462\u003c\/p\u003e \u003cp\u003e14.8 Exercises 467\u003c\/p\u003e \u003cp\u003eAppendix A: Answers to Even-Numbered Exercises 469\u003c\/p\u003e \u003cp\u003eReferences 473\u003c\/p\u003e \u003cp\u003eIndex 475\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49407155863895,"sku":"9781119795629","price":153.9,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119795629.jpg?v=1791469819"},{"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":42.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030518172.jpg?v=1791480494"}],"url":"https:\/\/bookcurl.com\/collections\/differential-and-riemannian-geometry.oembed?page=7","provider":"Book Curl","version":"1.0","type":"link"}