Differential and Riemannian geometry Books
Springer Geometry Fields and Cosmology Techniques and Applications 88 Fundamental Theories of Physics
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£170.99
Springer Convex and Starlike Mappings in Several Complex Variables 435 Mathematics and Its Applications
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£44.99
Springer Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds
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£85.49
Springer New Developments in Differential Geometry Budapest 1996 Proceedings of the Conference on Differential Geometry Budapest Hungary July 2730 1996
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£85.49
Springer Meromorphic Functions and Projective Curves 464 Mathematics and Its Applications
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£85.49
Springer Fundamentals of Finslerian Diffusion with Applications 101 Fundamental Theories of Physics
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£123.49
Springer Reduction of Nonlinear Control Systems A Differential Geometric Approach 472 Mathematics and Its Applications
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£44.99
Springer Smooth Quasigroups and Loops 492 Mathematics and Its Applications
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£44.99
Springer Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations 507 Mathematics and Its Applications
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£123.49
Springer Differential Geometry of Spray and Finsler Spaces
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£85.49
Springer Noncommutative Differential Geometry and Its Applications to Physics Proceedings of the Workshop at Shonan Japan June 1999 23 Mathematical Physics Studies
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£123.49
Springer London Geodesic and Horocyclic Trajectories
Book SynopsisGeodesic and Horocyclic Trajectories presents an introduction to the topological dynamics of two classical flows associated with surfaces of curvature −1, namely the geodesic and horocycle flows.Table of ContentsDynamics of Fuchsian groups.- Examples of Fuchsian Groups.- Topological dynamics of the geodesic flow.- Schottky groups.- Topological dynamics.- The Lorentzian point of view.- Trajectories and Diophantine approximations.
£54.99
Deductive Press Introduction to Arithmetic Groups
£14.87
Deductive Press Introduction to Arithmetic Groups
£22.03
LEGARE STREET PR An Introduction To Differential GeometryWith Use Of The Tensor Calculus
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£25.60
Legare Street Press Des Surfaces
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£22.75
Legare Street Press Anwendung Der Ausdehnungslehre Auf Die Allgemeine Theorie Der Raumkurven Und Krummen Flächen
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£22.75
Legare Street Press Leçons sur la théorie générale des surfaces et les applications géométriques du calcul infinitésimal Tome 3
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£30.35
Legare Street Press A A Treatise on the Geometry of Surfaces
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£25.60
Legare Street Press Papers on Space Analysis
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£24.65
Legare Street Press Theory of Cusped Geometries. I
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£22.75
Legare Street Press Vorlesungen über Differentialgeometrie autorisierte deutsche Übersetzung von Prof. Max Lukat
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£37.00
Legare Street Press Neue Geometrie Des Raumes
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£26.55
Legare Street Press Geometrie Der Berührungstransformationen Volume 1
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£35.10
Legare Street Press Applications Danalyse Et De Géométrie Qui Ont Servi En 1822 De Principal Fondement Au Traité Des Propriétés Projectives Des Figures Volume 1
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£31.30
Creative Media Partners, LLC Die Darstellende Geometrie Im Sinne Der Neueren Geometrie
£30.35
Creative Media Partners, LLC Die Darstellende Geometrie Im Sinne Der Neueren Geometrie
£22.75
Creative Media Partners, LLC Notions GÃcomÃctriques Sur Les Mouvements Et Transformations Ou ÃlÃcments De CinÃcmatique. Leçons De MÃccanique Pratique.
£18.95
Creative Media Partners, LLC Principes Et DÃcveloppements De GÃcomÃctrie CinÃcmatique
£32.25
Springer Science+Business Media An Introduction to Manifolds
Book SynopsisManifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory.Trade ReviewFrom the reviews of the second edition:“This book could be called a prequel to the book ‘Differential forms in algebraic topology’ by R. Bott and the author. Assuming only basic background in analysis and algebra, the book offers a rather gentle introduction to smooth manifolds and differential forms offering the necessary background to understand and compute deRham cohomology. … The text also contains many exercises … for the ambitious reader.” (A. Cap, Monatshefte für Mathematik, Vol. 161 (3), October, 2010)Table of ContentsPreface to the Second Edition.- Preface to the First Edition.-Chapter 1. Eudlidean Spaces. 1. Smooth Functions on a Euclidean Space.- 2. Tangent Vectors in R(N) as Derivativations.- 3. The Exterior Algebra of Multicovectors.- 4. Differential Forms on R(N).- Chapter 2. Manifolds.- 5. Manifolds.- 6. Smooth Maps on a Manifold.- 7. Quotients.- Chapter 3. The Tangent Space.- 8. The Tangent Space.- 9. Submanifolds.- 10. Categories and Functors.- 11. The Rank of a Smooth Map.- 12. The Tangent Bundle.- 13. Bump Functions and Partitions of Unity.- 14. Vector Fields.-Chapter 4. Lie Groups and Lie Algebras.- 15. Lie Groups.- 16. Lie Algebras.- Chapter 5. Differential Forms.- 17. Differential 1-Forms.- 18. Differential k-Forms.- 19. The Exterior Derivative.- 20. The Lie Derivative and Interior Multiplication.- Chapter 6. Integration.- 21. Orientations.- 22. Manifolds with Boundary.- 23. Integration on Manifolds.- Chapter 7. De Rham Theory.- 24. De Rham Cohomology.- 25. The Long Exact Sequence in Cohomology.- 26. The Mayer –Vietoris Sequence.- 27. Homotopy Invariance.- 28. Computation of de Rham Cohomology.- 29. Proof of Homotopy Invariance.-Appendices.- A. Point-Set Topology.- B. The Inverse Function Theorem on R(N) and Related Results.- C. Existence of a Partition of Unity in General.- D. Linear Algebra.- E. Quaternions and the Symplectic Group.- Solutions to Selected Exercises.- Hints and Solutions to Selected End-of-Section Problems.- List of Symbols.- References.- Index.
£44.99
Springer-Verlag New York Inc. Introduction to Smooth Manifolds
Book SynopsisThis book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer.This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theTrade ReviewFrom the reviews of the second edition:“It starts off with five chapters covering basics on smooth manifolds up to submersions, immersions, embeddings, and of course submanifolds. … the book under review is laden with excellent exercises that significantly further the reader’s understanding of the material, and Lee takes great pains to motivate everything well all the way through … . a fine graduate-level text for differential geometers as well as people like me, fellow travelers who always wish they knew more about such a beautiful subject.” (Michael Berg, MAA Reviews, October, 2012)Table of ContentsPreface.- 1 Smooth Manifolds.- 2 Smooth Maps.- 3 Tangent Vectors.- 4 Submersions, Immersions, and Embeddings.- 5 Submanifolds.- 6 Sard's Theorem.- 7 Lie Groups.- 8 Vector Fields.- 9 Integral Curves and Flows.- 10 Vector Bundles.- 11 The Cotangent Bundle.- 12 Tensors.- 13 Riemannian Metrics.- 14 Differential Forms.- 15 Orientations.- 16 Integration on Manifolds.- 17 De Rham Cohomology.- 18 The de Rham Theorem.- 19 Distributions and Foliations.- 20 The Exponential Map.- 21 Quotient Manifolds.- 22 Symplectic Manifolds.- Appendix A: Review of Topology.- Appendix B: Review of Linear Algebra.- Appendix C: Review of Calculus.- Appendix D: Review of Differential Equations.- References.- Notation Index.- Subject Index
£59.99
Read Books Plane And Solid Analytic Geometry
£28.49
Springer First Steps in Differential Geometry
Book SynopsisBasic Objects and Notation.- Linear Algebra Essentials.- Advanced Calculus.- Differential Forms and Tensors.- Riemannian Geometry.- Contact Geometry.- Symplectic Geometry.- References.- Index.Trade ReviewFrom the book reviews:“This books presents an alternative route, aiming to provide the student with an introduction not only to Riemannian geometry, but also to contact and symplectic geometry. … the book is leavened with an excellent collection of illustrative examples, and a wealth of exercises on which students can hone their skills. Each chapter also includes a short guide to further reading on the topic with a helpful brief commentary on the suggestions.” (Robert J. Low, Mathematical Reviews, May, 2014)“This book is a distinctive and ambitious effort to bring modern notions of differential geometry to undergraduates. … Mclnerney’s writing is well constructed and very clear … . Summing Up: Recommended. Upper-division undergraduates and graduate students.” (S. J. Colley, Choice, Vol. 51 (8), April, 2014)“The author does make a considerable effort to keep things as accessible as possible, with fairly detailed explanations, extensive motivational discussions and homework problems … . this book provides a different way of looking at the subject of differential geometry, one that is more modern and sophisticated than is provided by many of the standard undergraduate texts and which will certainly do a good job of preparing the student for additional work in this area down the road.” (Mark Hunacek, MAA Reviews, January, 2014)“This text provides an early and broad view of geometry to mathematical students … . Altogether, this book is easy to read because there are plenty of figures, examples and exercises which make it intuitive and perfect for undergraduate students.” (Teresa Arias-Marco, zbMATH, Vol. 1283, 2014)Table of ContentsBasic Objects and Notation.- Linear Algebra Essentials.- Advanced Calculus.- Differential Forms and Tensors.- Riemannian Geometry.- Contact Geometry.- Symplectic Geometry.- References.- Index.
£48.59
Minkowski Institute Press Differential Geometry: 1972 Lecture Notes
£13.66
Springer Nature Switzerland AG From Differential Geometry to Non-commutative
Book SynopsisThis 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.Trade Review“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)Table of Contents1. 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.
£104.49
Springer Nature Switzerland AG Extrinsic Geometry of Foliations
Book SynopsisThis book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry. The concept of mixed curvature is central to the discussion, and a version of the deep problem of the Ricci curvature for the case of mixed curvature of foliations is examined. The book is divided into five chapters that deal with integral and variation formulas and curvature and dynamics of foliations. Different approaches and methods (local and global, regular and singular) in solving the problems are described using integral and variation formulas, extrinsic geometric flows, generalizations of the Ricci and scalar curvatures, pseudo-Riemannian and metric-affine geometries, and 'computable' Finsler metrics.The book presents the state of the art in geometric and analytical theory of foliations as a continuation of the authors' life-long work in extrinsic geometry. It is designed for newcomers to the field as well as experienced geometers working in Riemannian geometry, foliation theory, differential topology, and a wide range of researchers in differential equations and their applications. It may also be a useful supplement to postgraduate level work and can inspire new interesting topics to explore.Trade Review“The reader is assumed to have some background in topology and differential geometry. The book is a continuation of the authors’ work in extrinsic geometry and thus provides a useful reference for researchers in this field.” (Emanuel-Ciprian Cismaş, zbMATH 1479.53002, 2022)Table of ContentsPreface.- 1. Preliminaries.- 2. Integral formulas.- 3. Prescribing the mean curvature.- 4. Variational formulae.- 5. Extrinsic Geometric flows.- References.- Index.
£66.49
Springer Nature Switzerland AG Comparison Finsler Geometry
Book SynopsisThis monograph presents recent developments in comparison geometry and geometric analysis on Finsler manifolds. Generalizing the weighted Ricci curvature into the Finsler setting, the author systematically derives the fundamental geometric and analytic inequalities in the Finsler context. Relying only upon knowledge of differentiable manifolds, this treatment offers an accessible entry point to Finsler geometry for readers new to the area. Divided into three parts, the book begins by establishing the fundamentals of Finsler geometry, including Jacobi fields and curvature tensors, variation formulas for arc length, and some classical comparison theorems. Part II goes on to introduce the weighted Ricci curvature, nonlinear Laplacian, and nonlinear heat flow on Finsler manifolds. These tools allow the derivation of the Bochner–Weitzenböck formula and the corresponding Bochner inequality, gradient estimates, Bakry–Ledoux’s Gaussian isoperimetric inequality, and functional inequalities in the Finsler setting. Part III comprises advanced topics: a generalization of the classical Cheeger–Gromoll splitting theorem, the curvature-dimension condition, and the needle decomposition. Throughout, geometric descriptions illuminate the intuition behind the results, while exercises provide opportunities for active engagement. Comparison Finsler Geometry offers an ideal gateway to the study of Finsler manifolds for graduate students and researchers. Knowledge of differentiable manifold theory is assumed, along with the fundamentals of functional analysis. Familiarity with Riemannian geometry is not required, though readers with a background in the area will find their insights are readily transferrable.Trade Review“Finsler geometry is an active area of research in mathematics and has led to numerous real-world applications. This book is a comprehensive introduction to Finsler geometry and its applications. It covers the basic concepts of this geometry. More intuitively, this book provides an accessible introduction to recent developments in comparison geometry and geometric analysis on Finsler manifolds. … this book offers a valuable perspective for those familiar with comparison geometry and geometric analysis.” (Behroz Bidabad, Mathematical Reviews, May, 2023)Table of ContentsI Foundations of Finsler Geometry.- 1. Warm-up: Norms and inner products.- 2. Finsler manifolds.- 3. Properties of geodesics.- 4. Covariant derivatives.- 5. Curvature.- 6. Examples of Finsler manifolds.- 7. Variation formulas for arclength.- 8. Some comparison theorems.- II Geometry and analysis of weighted Ricci curvature.- 9. Weighted Ricci curvature.- 10. Examples of measured Finsler manifolds.- 11. The nonlinear Laplacian.- 12. The Bochner-Weitzenbock formula.- 13. Nonlinear heat flow.- 14. Gradient estimates.- 15. Bakry-Ledoux isoperimetric inequality.- 16. Functional inequalities.- III Further topics.- 17. Splitting theorems.- 18. Curvature-dimension condition.- 19. Needle decompositions.
£85.49
Springer Nature Switzerland AG Differential Geometry
Book SynopsisThis book combines the classical and contemporary approaches to differential geometry. An introduction to the Riemannian geometry of manifolds is preceded by a detailed discussion of properties of curves and surfaces.The chapter on the differential geometry of plane curves considers local and global properties of curves, evolutes and involutes, and affine and projective differential geometry. Various approaches to Gaussian curvature for surfaces are discussed. The curvature tensor, conjugate points, and the Laplace-Beltrami operator are first considered in detail for two-dimensional surfaces, which facilitates studying them in the many-dimensional case. A separate chapter is devoted to the differential geometry of Lie groups.Trade Review“All chapters are supplemented with solutions of the problems scattered throughout the text. Designed as a text for a lecturer course on the subject, it is perfect and can be recommended for students interested in this classical field.” (Ivailo. M. Mladenov, zbMATH 1498.53001, 2022)Table of ContentsCurves in the Plane.- Curves in Space.- Surfaces in Space.- Hypersurfaces in Rn+1.- Connections.- Riemannian Manifolds.- Lie Groups.- Comparison Theorems.- Curvature and Topology.- Laplacian.- Appendix.- Bibliography.- Index.
£37.49
Springer Discrete Isothermic Surfaces in Lie Sphere
Book SynopsisChapter 1. Introduction.- Chapter 2.Isothermic surfaces in Möbius geometry.- Chapter 3. From smooth to discrete via permutability.- Chapter 4. Discrete Isothermic surfaces.- Chapter 5. ?-surfaces in Lie sphere geometry.- Chapter 6. Integrability of ?-surfaces via isothermicity.- Chapter 7. Discrete ?-surfaces.
£64.99
Springer Geometry of Integrable Systems
Book SynopsisPart I: Preliminary material.- Symplectic Geometry.- Elements of Poisson Geometry.- Hamiltonian G-actions and the Marsden-Weinstein-Meyer reduction.- Lagrangian fibrations and integrable systems.- Elements of Bi-Hamiltonian Geometry.- Bibliographical Notes.- Part II: A Sample of Classical Integrable Systems.- Rigid bodies.- The Toda System.- Calogero-Moser Systems.- Appendix A: Elements of Symplectic Linear Algebra.- Appendix B: Elements of Differential Geometry.- Appendix C: Lie Groups, Lie Algebras, and Fiber Bundles.- Appendix D: Cotangent Lifts.- Bibliography.- Index.
£54.99
De Gruyter Riemannian Geometry
Book SynopsisThe series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures, and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational Models for Fractional Calculus, second edition (2020) Mariusz Lemańczyk, Ergodic Theory: Spectral Theory, Joinings, and Their Applications (2020) Marco Abate, Holomorphic Dynamics on Hyperbolic Complex Manifolds (2021) Miroslava Antić, Joeri Van der Veken, and Luc Vrancken, Differential Geometry of Submanifolds: Submanifolds of Almost Complex Spaces and Almost Product Spaces (2021) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)
£138.22
Birkhauser Verlag AG Space-Time Algebra
Book SynopsisThis small book started a profound revolution in the development of mathematical physics, one which has reached many working physicists already, and which stands poised to bring about far-reaching change in the future.At its heart is the use of Clifford algebra to unify otherwise disparate mathematical languages, particularly those of spinors, quaternions, tensors and differential forms. It provides a unified approach covering all these areas and thus leads to a very efficient ‘toolkit’ for use in physical problems including quantum mechanics, classical mechanics, electromagnetism and relativity (both special and general) – only one mathematical system needs to be learned and understood, and one can use it at levels which extend right through to current research topics in each of these areas. These same techniques, in the form of the ‘Geometric Algebra’, can be applied in many areas of engineering, robotics and computer science, with no changes necessary – it is the same underlying mathematics, and enables physicists to understand topics in engineering, and engineers to understand topics in physics (including aspects in frontier areas), in a way which no other single mathematical system could hope to make possible.There is another aspect to Geometric Algebra, which is less tangible, and goes beyond questions of mathematical power and range. This is the remarkable insight it gives to physical problems, and the way it constantly suggests new features of the physics itself, not just the mathematics. Examples of this are peppered throughout ‘Space-Time Algebra’, despite its short length, and some of them are effectively still research topics for the future.From the Foreward by Anthony LasenbyTable of ContentsPreface to the Second Edition.- Introduction.- Part I:Geometric Algebra.- 1.Intrepretation of Clifford Algebra.- 2.Definition of Clifford Algebra.- 3.Inner and Outer Products.- 4.Structure of Clifford Algebra.- 5.Reversion, Scalar Product.- 6.The Algebra of Space.- 7.The Algebra of Space-Time.- Part II:Electrodynamics.- 8.Maxwell's Equation.- 9.Stress-Energy Vectors.- 10.Invariants .- 11. Free Fields.- Part III:Dirac Fields.- 12.Spinors.- 13.Dirac's Equation.- 14.Conserved Currents.- 15.C, P, T.- Part IV:Lorentz Transformations.- 16.Reflections and Rotations.- 17.Coordinate Transformations.- 18.Timelike Rotations.- 19.Scalar Product.- Part V:Geometric Calculus.- 20.Differentiation.- 21.Coordinate Transformations.- 22.Integration.- 23.Global and Local Relativity.- 24.Gauge Transformation and Spinor Derivatives.- Conclusion.- Appendices.- A.Bases and Pseudoscalars.- B.Some Theorems.- C.Composition of Spacial Rotations.- D.Matrix Representation of the Pauli Algebra.
£79.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Differential Geometric Methods in Mathematical Physics: Proceedings of the International Conference Held at the Technical University of Clausthal, Germany, July 1978
Book SynopsisOn a geometric quantization scheme generalizing those of Kostant-Souriau and Czyz.- Further applications of geometric quantization.- General vector field representations of local Heisenberg systems.- Aspects of relativistic quantum mechanics on phase space.- On the confinement of magnetic poles.- SU(3) and SU(4) as spectrum-generating groups.- The phase space for the Yang-Mills equations.- Instantons in nonlinear ?-models, gauge theories and general relativity.- Gauge-theoretical foundation of color geometrodynamics.- Non-associative algebras and exceptional gauge groups.- Atiyah-Singer index theorem and quantum field theory.- Topological concepts in phase transition theory.- Life without T2.- Affine model of internal degrees of freedom in a non-euclidean space.- Jet bundles and weyl geometry.- Line fields and Lorentz manifolds.- The manifold of embeddings of a closed manifold.- The manifold of embeddings of a non-compact manifold.Table of ContentsOn a geometric quantization scheme generalizing those of Kostant-Souriau and Czyz.- Further applications of geometric quantization.- General vector field representations of local Heisenberg systems.- Aspects of relativistic quantum mechanics on phase space.- On the confinement of magnetic poles.- SU(3) and SU(4) as spectrum-generating groups.- The phase space for the Yang-Mills equations.- Instantons in nonlinear ?-models, gauge theories and general relativity.- Gauge-theoretical foundation of color geometrodynamics.- Non-associative algebras and exceptional gauge groups.- Atiyah-Singer index theorem and quantum field theory.- Topological concepts in phase transition theory.- Life without T2.- Affine model of internal degrees of freedom in a non-euclidean space.- Jet bundles and weyl geometry.- Line fields and Lorentz manifolds.- The manifold of embeddings of a closed manifold.- The manifold of embeddings of a non-compact manifold.
£44.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Riemannian Geometry
Book SynopsisThis book covers the topics of differential manifolds, Riemannian metrics, connections, geodesics and curvature, with special emphasis on the intrinsic features of the subject. It treats in detail classical results on the relations between curvature and topology. The book features numerous exercises with full solutions and a series of detailed examples are picked up repeatedly to illustrate each new definition or property introduced.Trade ReviewFrom the reviews of the third edition: "This new edition maintains the clear written style of the original, including many illustrations … examples and exercises (most with solutions)." (Joseph E. Borzellino, Mathematical Reviews, 2005) "This book based on graduate course on Riemannian geometry … covers the topics of differential manifolds, Riemannian metrics, connections, geodesics and curvature, with special emphasis on the intrinsic features of the subject. Classical results … are treated in detail. … contains numerous exercises with full solutions and a series of detailed examples which are picked up repeatedly to illustrate each new definition or property introduced. For this third edition, some topics … have been added and worked out in the same spirit." (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 50, (3-4), 2004) "This book is based on a graduate course on Riemannian geometry and analysis on manifolds that was held in Paris. … Classical results on the relations between curvature and topology are treated in detail. The book is almost self-contained, assuming in general only basic calculus. It contains nontrivial exercises with full solutions at the end. Properties are always illustrated by many detailed examples." (EMS Newsletter, December 2005) "The guiding line of this by now classic introduction to Riemannian geometry is an in-depth study of each newly introduced concept on the basis of a number of reoccurring well-chosen examples … . The book continues to be an excellent choice for an introduction to the central ideas of Riemannian geometry." (M. Kunzinger, Monatshefte für Mathematik, Vol. 147 (1), 2006)Table of Contents1 Differential manifolds.- 1.A From submanifolds to abstract manifolds.- 1.A.1 Submanifolds of Euclidean spaces.- 1.A.2 Abstract manifolds.- 1.A.3 Smooth maps.- 1.B The tangent bundle.- 1.B.1 Tangent space to a submanifold of Rn+k.- 1.B.2 The manifold of tangent vectors.- 1.B.3 Vector bundles.- 1.B.4 Tangent map.- 1.C Vector fields.- 1.C.1 Definitions.- 1.C.2 Another definition for the tangent space.- 1.C.3 Integral curves and flow of a vector field.- 1.C.4 Image of a vector field by a diffeomorphism.- 1.D Baby Lie groups.- 1.D.1 Definitions.- 1.D.2 Adjoint representation.- 1.E Covering maps and fibrations.- 1.E.1 Covering maps and quotients by a discrete group.- 1.E.2 Submersions and fibrations.- 1.E.3 Homogeneous spaces.- 1.F Tensors.- 1.F.1 Tensor product (a digest).- 1.F.2 Tensor bundles.- 1.F.3 Operations on tensors.- 1.F.4 Lie derivatives.- 1.F.5 Local operators, differential operators.- 1.F.6 A characterization for tensors.- 1.G. Differential forms.- 1.G.1 Definitions.- 1.G.2 Exterior derivative.- 1.G.3 Volume forms.- 1.G.4 Integration on an oriented manifold.- 1.G.5 Haar measure on a Lie group.- 1.H Partitions of unity.- 2 Riemannian metrics.- 2.A Existence theorems and first examples.- 2.A.1 Basic definitions.- 2.A.2 Submanifolds of Euclidean or Minkowski spaces.- 2.A.3 Riemannian submanifolds, Riemannian products.- 2.A.4 Riemannian covering maps, flat tori.- 2.A.5 Riemannian submersions, complex projective space.- 2.A.6 Homogeneous Riemannian spaces.- 2.B Covariant derivative.- 2.B.1 Connections.- 2.B.2 Canonical connection of a Riemannian submanifold.- 2.B.3 Extension of the covariant derivative to tensors.- 2.B.4 Covariant derivative along a curve.- 2.B.5 Parallel transport.- 2.B.6 natural metric on the tangent bundle.- 2.C Geodesies.- 2.C.1 Definition, first examples.- 2.C.2 Local existence and uniqueness for geodesies, exponential map.- 2.C.3 Riemannian manifolds as metric spaces.- 2.C.4 An invitation to isosystolic inequalities.- 2.C.5 Complete Riemannian manifolds, Hopf-Rinow theorem.- 2.C.6 Geodesies and submersions, geodesies of PnC.- 2.C.7 Cut-locus.- 2.C.8 The geodesic flow.- 2.D A glance at pseudo-Riemannian manifolds.- 2.D.1 What remains true?.- 2.D.2 Space, time and light-like curves.- 2.D.3 Lorentzian analogs of Euclidean spaces, spheres and hegeode spaces.- 2.D.4 (In)completeness.- 2.D.5 The Schwarzschild model.- 2.D.6 Hyperbolicity versus ellipticity.- 3 Curvature.- 3.A. The curvature tensor.- 3.A.1 Second covariant derivative.- 3.A.2 Algebraic properties of the curvature tensor.- 3.A.3 Computation of curvature: some examples.- 3.A.4 Ricci curvature, scalar curvature.- 3.B. First and second variation.- 3.B.1 Technical preliminaries.- 3.B.2 First variation formula.- 3.B.3 Second variation formula.- 3.C. Jacobi vector fields.- 3.C.1 Basic topics about second derivatives.- 3.C.2 Index form.- 3.C.3 Jacobi fields and exponential map.- 3.C.4 Applications.- 3.D. Riemannian submersions and curvature.- 3.D.1 Riemannian submersions and connections.- 3.D.2 Jacobi fields of PnC.- 3.D.3 O’Neill’s formula.- 3.D.4 Curvature and length of small circles. Application to Riemannian submersions.- 3.E. The behavior of length and energy in the neighborhood of a geodesic.- 3.E.1 Gauss lemma.- 3.E.2 Conjugate points.- 3.E.3 Some properties of the cut-locus.- 3.F Manifolds with constant sectional curvature.- 3.G Topology and curvature: two basic results.- 3.G.1 Myers’ theorem.- 3.G.2 Cartan-Hadamard’s theorem.- 3.H. Curvature and volume.- 3.H.1 Densities on a differentiable manifold.- 3.H.2 Canonical measure of a Riemannian manifold.- 3.H.3 Examples: spheres, hyperbolic spaces, complex projective spaces.- 3.H.4 Small balls and scalar curvature.- 3.H.5 Volume estimates.- 3.I. Curvature and growth of the fundamental group.- 3.I.1 Growth of finite type groups.- 3.I.2 Growth of the fundamental group of compact manifolds with negative curvature.- 3.J. Curvature and topology: some important results.- 3.J.1 Integral formulas.- 3.J.2 (Geo)metric methods.- 3.J.3 Analytic methods.- 3.J.4 Coarse point of view: compactness theorems.- 3.K. Curvature tensors and representations of the orthogonal group.- 3.K.1 Decomposition of the space of curvature tensors.- 3.K.2 Conformally flat manifolds.- 3.K.3 The Second Bianchi identity.- 3.L. Hyperbolic geometry.- 3.L.1 Introduction.- 3.L.2 Angles and distances in the hyperbolic plane.- 3.L.3 Polygons with “many” right angles.- 3.L.4 Compact surfaces.- 3.L.5 Hyperbolic trigonometry.- 3.L.6 Prescribing constant negative curvature.- 3.L.7 A few words about higher dimension.- 3.M. Conformai geometry.- 3.M.2 Introduction.- 3.M.3 The Möbius group.- 3.M.4 Conformai, elliptic and hyperbolic geometry.- 4 Analysis on manifolds.- 4.A. Manifolds with boundary.- 4.A.1 Introduction.- 4.A.2 Stokes theorem and integration by parts.- 4.B. Bishop inequality.- 4.B.1 Some commutation formulas.- 4.B.2 Laplacian of the distance function.- 4.B.3 Another proof of Bishop’s inequality.- 4.B.4 Heintze-Karcher inequality.- 4.C. Differential forms and cohomology.- 4.C.1 The de Rham complex.- 4.C.2 Differential operators and their formal adjoints.- 4.C.3 The Hodge-de Rham theorem.- 4.C.4 A second visit to the Bochner method.- 4.D. Basic spectral geometry.- 4.D.1 The Laplace operator and the wave equation.- 4.D.2 Statement of basic results on the spectrum.- 4.E. Some examples of spectra.- 4.E.1 Introduction.- 4.E.2 The spectrum of flat tori.- 4.E.3 Spectrum of (Sn, can).- 4.F The minimax principle.- 4.G Eigenvalues estimates.- 4.G.1 Introduction.- 4.G.2 Bishop’s inequality and coarse estimates.- 4.G.3 Some consequences of Bishop’s theorem.- 4.G.4 Lower bounds for the first eigenvalue.- 4.H. Paul Levy’s isoperimetric inequality.- 4.H.1 The statement.- 4.H.2 The proof.- 5 Riemannian submanifolds.- 5.A. Curvature of submanifolds.- 5.A.1 Second fundamental form.- 5.A.2 Curvature of hypersurfaces.- 5.A.3 Application to explicit computations of curvatures.- 5.B Curvature and convexity.- 5.C Minimal surfaces.- 5.C.1 First results.- 5.C.2 Surfaces with constant mean curvature.- A Some extra problems.- B Solutions of exercises.- List of figures.
£59.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Bryce DeWitt's Lectures on Gravitation: Edited by Steven M. Christensen
Book SynopsisBryce DeWitt, a student of Nobel Laureate Julian Schwinger, was himself one of the towering figures in 20th century physics, particularly renowned for his seminal contributions to quantum field theory, numerical relativity and quantum gravity. In late 1971 DeWitt gave a course on gravitation at Stanford University, leaving almost 400 pages of detailed handwritten notes. Written with clarity and authority, and edited by his former student Steven Christensen, these timeless lecture notes, containing material or expositions not found in any other textbooks, are a gem to be discovered or re-discovered by anyone seriously interested in the study of gravitational physics.Trade ReviewFrom the reviews:“DeWitt’s lectures cover interesting and detailed material which is rarely found in other text books. It is a book for the advanced reader.” (Norbert Dragon, General Relativity and Gravitation, Vol. 44, 2012)Table of ContentsReview of the Uses of Invariants in Special Relativity.- Accelerated Motion in Special Relativity.- Realization of Continuous Groups.- Riemannian Manifolds.- The Free Particle Geodesics.- Weak Field Approximation. Newton`s Theory.- Ensembles of Particles.- Production of Gravitational Fields by Matter.- Conservation Laws.- Phenomenological Description of a Conservative Continuous Medium.- Solubility of the Einstein and Matter Equations.- Energy, Momentum and Stress in the Gravitational Field.- Measurement of Asymptotic Field.- The Electromagnetic Field.- Gravitational Waves.- Spinning Bodies.- Weak Field Gravitational Wave.- Stationary Spherically (or Rotationally) Symmetric Metric.- Kerr Metric Subcalculations.- Friedmann Cosmology.- Dynamical Equations and Diffeomorphisms.
£64.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Lectures on Symplectic Geometry
Book SynopsisThese notes approximately transcribe a 15-week course on symplectic geometry I taught at UC Berkeley in the Fall of 1997. The course at Berkeley was greatly inspired in content and style by Victor Guillemin, whose masterly teaching of beautiful courses on topics related to s- plectic geometry at MIT, I was lucky enough to experience as a graduate student. I am very thankful to him! That course also borrowed from the 1997 Park City summer courses on symplectic geometry and topology, and from many talks and discussions of the symplectic geometry group at MIT. Among the regular participants in the MIT - formal symplectic seminar 93-96, I would like to acknowledge the contributions of Allen Knutson, Chris Woodward, David Metzler, Eckhard Meinrenken, Elisa Prato, Eugene Lerman, Jonathan Weitsman, Lisa Jeffrey, Reyer Sjamaar, Shaun Martin, Stephanie Singer, Sue Tolman and, last but not least, Yael Karshon. Thanks to everyone sitting in Math 242 in the Fall of 1997 for all the c- ments they made, and especially to those who wrote notes on the basis of which I was better able to reconstruct what went on: Alexandru Scorpan, Ben Davis, David Martinez,DonBarkauskas,EzraMiller,HenriqueBursztyn,John-PeterLund,Laura De Marco, Olga Radko, Peter P? rib' ?k, Pieter Collins, Sarah Packman, Stephen Bigelow, Susan Harrington, Tolga Etgu .. and Yi Ma.Trade Review“I find this to be both the best introduction to symplectic geometry as well as a model for how to introduce any field of study. … one feels the hand of a master in the text’s homework sets: concrete, illustrative, and enhancing the material presented. … For an upper-level undergraduate or beginning graduate student, Lectures on Symplectic Geometry remains, in my opinion, an ideal starting point into an exciting, active and growing area of mathematics.” (Andrew McInerney, MAA Reviews, June, 2018)From the reviews of the first printing Over the years, there have been several books written to serve as an introduction to symplectic geometry and topology, […] The text under review here fits well within this tradition, providing a useful and effective synopsis of the basics of symplectic geometry and possibly serving as the springboard for a prospective researcher. The material covered here amounts to the "usual suspects" of symplectic geometry and topology. From an introductory chapter of symplectic forms and symplectic algebra, the book moves on to many of the subjects that serve as the basis for current research:symplectomorphisms, Lagrangian submanifolds, the Moser theorems, Darboux-Moser-Weinstein theory, almost complex structures, Kãhler structures, Hamiltonian mechanics, symplectic reduction, etc. The text is written in a clear, easy-to-follow style, that is most appropriate in mathematical sophistication for second-year graduate students; […]. This text had its origins in a 15-week course that the author taught at UC Berkeley. There are some nice passages where the author simply lists some known results and some well-known conjectures, much as one would expect to see in a good lecture on the same subject. Particularly eloquent is the author’s discussion of the compact examples and counterexamples of symplectic, almost complex, complex and Kähler manifolds. Throughout the text, she uses specific, well-chosen examples to illustrate the results. In the initial chapter, she provides a detailed section on the classical example of the syrnplectic structure of the cotangent bundle of a manifold. Showing a good sense of pedagogy, the author often leaves these examples as well-planned homework assignments at the end of some of the sections. […] In all of these cases, the author gives the reader a chance to illustrate and understand the interesting results of each section, rather than relegating the tedious but needed results to the reader. Mathematical Reviews 2002iTable of ContentsSymplectic Manifolds.- Symplectic Forms.- Symplectic Form on the Cotangent Bundle.- Symplectomorphisms.- Lagrangian Submanifolds.- Generating Functions.- Recurrence.- Local Forms.- Preparation for the Local Theory.- Moser Theorems.- Darboux-Moser-Weinstein Theory.- Weinstein Tubular Neighborhood Theorem.- Contact Manifolds.- Contact Forms.- Contact Dynamics.- Compatible Almost Complex Structures.- Almost Complex Structures.- Compatible Triples.- Dolbeault Theory.- Kähler Manifolds.- Complex Manifolds.- Kähler Forms.- Compact Kähler Manifolds.- Hamiltonian Mechanics.- Hamiltonian Vector Fields.- Variational Principles.- Legendre Transform.- Moment Maps.- Actions.- Hamiltonian Actions.- Symplectic Reduction.- The Marsden-Weinstein-Meyer Theorem.- Reduction.- Moment Maps Revisited.- Moment Map in Gauge Theory.- Existence and Uniqueness of Moment Maps.- Convexity.- Symplectic Toric Manifolds.- Classification of Symplectic Toric Manifolds.- Delzant Construction.- Duistermaat-Heckman Theorems.
£49.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Differential Geometry in the Large: Seminar Lectures New York University 1946 and Stanford University 1956
Book SynopsisThese notes consist of two parts: Selected in York 1) Geometry, New 1946, Topics University Notes Peter Lax. by Differential in the 2) Lectures on Stanford Geometry Large, 1956, Notes J.W. University by Gray. are here with no essential They reproduced change. Heinz was a mathematician who mathema- Hopf recognized important tical ideas and new mathematical cases. In the phenomena through special the central idea the of a or difficulty problem simplest background is becomes clear. in this fashion a crystal Doing geometry usually lead serious allows this to to - joy. Hopf's great insight approach for most of the in these notes have become the st- thematics, topics I will to mention a of further try ting-points important developments. few. It is clear from these notes that laid the on Hopf emphasis po- differential Most of the results in smooth differ- hedral geometry. whose is both t1al have understanding geometry polyhedral counterparts, works I wish to mention and recent important challenging. Among those of Robert on which is much in the Connelly rigidity, very spirit R. and in - of these notes (cf. Connelly, Conjectures questions open International of Mathematicians, H- of gidity, Proceedings Congress sinki vol. 1, 407-414) 1978, .Table of ContentsSelected Topics in Geometry.- The Euler Characteristic and Related Topics.- Selected Topics in Elementary Differential Geometry.- The Isoperimetric Inequality and Related Inequalities.- The Elementary Concept of Area and Volume.- Differential Geometry in the Large.- Differential Geometry of Surfaces in the Small.- Some General Remarks on Closed Surfaces in Differential Geometry.- The Total Curvature (Curvatura Inteqra) of a Closed Surface with Riemannian Metric and Poincaré’s Theorem on the Singularities of Fields of Line Elements.- Hadamard’s Characterization of the Ovaloids.- Closed Surfaces with Constant Gauss Curvature (Hilbert’s Method) — Generalizations and Problems — General Remarks on Weinqarten Surfaces.- General Closed Surfaces of Genus O with Constant Mean Curvature — Generalizations.- Simple Closed Surfaces (of Arbitrary Genus) with Constant Mean Curvature — Generalizations.- The Congruence Theorem for Ovaloids.- Singularities of Surfaces with Constant Negative Gauss Curvature.
£27.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Complex Geometry and Analysis: Proceedings of the International Symposium in honour of Edoardo Vesentini, held in Pisa (Italy), May 23 - 27, 1988
Book SynopsisThe volume contains the texts of the main talks delivered at the International Symposium on Complex Geometry and Analysis held in Pisa, May 23-27, 1988. The Symposium was organized on the occasion of the sixtieth birthday of Edoardo Vesentini. The aim of the lectures was to describe the present situation, the recent developments and research trends for several relevant topics in the field. The contributions are by distinguished mathematicians who have actively collaborated with the mathematical school in Pisa over the past thirty years.Table of ContentsHyperkähler manifolds.- Affine differential geometry and holomorphic curves.- The meromorphic continuation of Kloosterman-Selberg zeta functions.- Deformation of compact Riemann surfaces Y of genus p with distinguished points P 1 …, P m ? Y.- On moduli of vector bundles.- Quasiconformal mappings on CR manifolds.- On the stability of positive semigroups generated by operator matrices.- The levi problem on algebraic manifolds.- A Banach-Steinhaus theorem for weak and order continuous operators.- Fixed points of holomorphic mappings.
£22.99
