Differential and Riemannian geometry Books
Springer Lagrangian Floer Theory and Its Deformations
Book SynopsisBased Loop Space and A8 Space.- A8 Algebras and Modules: Unfiltered Case.- Obstruction-Deformation Theory of Filtered A8 Bimodules.- Symplectic Geometry and Hamiltonian Dynamics.- Analysis of Pseudoholomorphic Curves and Bordered Stable Maps.- Critical Points of Potential Functions and Floer Cohomology.- Filtered Fukaya Category and its Bulk Deformations.
£71.24
Springer Differential Geometry
Book SynopsisChapter 1 Manifolds and Tensor Calculus.- Chapter 2 Differentiable Actions and Principal Bundles.- Chapter 3 Infinite dimensional Differential Geometry.
£134.99
Springer London Ltd Matrix Groups: An Introduction to Lie Group
Book SynopsisThis book offers a first taste of the theory of Lie groups, focusing mainly on matrix groups: closed subgroups of real and complex general linear groups. The first part studies examples and describes classical families of simply connected compact groups. The second section introduces the idea of a lie group and explores the associated notion of a homogeneous space using orbits of smooth actions. The emphasis throughout is on accessibility. Trade ReviewFrom the reviews of the first edition: MATHEMATICAL REVIEWS "This excellent book gives an easy introduction to the theory of Lie groups and Lie algebras by restricting the material to real and complex matrix groups. This provides the reader not only with a wealth of examples, but it also makes the key concepts much more concrete. This combination makes the material in this book more easily accessible for the readers with a limited background…The book is very easy to read and suitable for an elementary course in Lie theory aimed at advanced undergraduates or beginning graduate students…To summarize, this is a well-written book, which is highly suited as an introductory text for beginning graduate students without much background in differential geometry or for advanced undergraduates. It is a welcome addition to the literature in Lie theory." "This book is an introduction to Lie group theory with focus on the matrix case. … This book can be recommended to students, making Lie group theory more accessible to them." (A. Akutowicz, Zentralblatt MATH, Vol. 1009, 2003)Table of ContentsI. Basic Ideas and Examples.- 1. Real and Complex Matrix Groups.- 2. Exponentials, Differential Equations and One-parameter Subgroups.- 3. Tangent Spaces and Lie Algebras.- 4. Algebras, Quaternions and Quaternionic Symplectic Groups.- 5. Clifford Algebras and Spinor Groups.- 6. Lorentz Groups.- II. Matrix Groups as Lie Groups.- 7. Lie Groups.- 8. Homogeneous Spaces.- 9. Connectivity of Matrix Groups.- III. Compact Connected Lie Groups and their Classification.- 10. Maximal Tori in Compact Connected Lie Groups.- 11. Semi-simple Factorisation.- 12. Roots Systems, Weyl Groups and Dynkin Diagrams.- Hints and Solutions to Selected Exercises.
£29.99
Taylor & Francis Ltd Inverse Boundary Spectral Problems Monographs and Surveys in Pure and Applied Mathematics
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£58.89
Taylor & Francis Ltd Classical and Discrete Differential Geometry
Book SynopsisThis book introduces differential geometry and cutting-edge findings from the discipline by incorporating both classical approaches and modern discrete differential geometry across all facets and applications, including graphics and imaging, physics and networks.With curvature as the centerpiece, the authors present the development of differential geometry, from curves to surfaces, thence to higher dimensional manifolds; and from smooth structures to metric spaces, weighted manifolds and complexes, and to images, meshes and networks. The first part of the book is a differential geometric study of curves and surfaces in the Euclidean space, enhanced while the second part deals with higher dimensional manifolds centering on curvature by exploring the various ways of extending it to higher dimensional objects and more general structures and how to return to lower dimensional constructs. The third part focuses on computational algorithms in algebraic topology and conformal geometry, applicable for surface parameterization, shape registration and structured mesh generation.The volume will be a useful reference for students of mathematics and computer science, as well as researchers and engineering professionals who are interested in graphics and imaging, complex networks, differential geometry and curvature.Table of ContentsSection I Differential Geometry, Classical and Discrete 1. Curves 2. Surfaces: Gauss Curvature – First Definition 3. Metrization of Gauss Curvature 4. Gauss Curvature and Theorema Egregium 5. The Mean and Gauss Curvature Flows 6. Geodesics 7. Geodesics and Curvature 8. The Equations of Compatibility 9. The Gauss-Bonnet Theorem and the Poincare Index Theorem 10. Higher Dimensional Curvatures 11. Higher Dimensional Curvatures 12. Discrete Ricci Curvature and Flow 13. Weighted Manifolds and Ricci Curvature Revisited Section II Differential Geometry, Computational Aspects 14. Algebraic Topology 15. Homology and Cohomology Group 16. Exterior Calculus and Hodge Decomposition 17. Harmonic Map 18. Riemann Surface 19. Conformal Mapping 20. Discrete Surface Curvature Flows 21. Mesh Generation Based on Abel-Jacobi Theorem Section III Appendices 22. Appendix A 23. Appendix B 24. Appendix C
£95.00
Taylor & Francis Ltd Classical and Discrete Differential Geometry
Book SynopsisThis book introduces differential geometry and cutting-edge findings from the discipline by incorporating both classical approaches and modern discrete differential geometry across all facets and applications, including graphics and imaging, physics and networks.With curvature as the centerpiece, the authors present the development of differential geometry, from curves to surfaces, thence to higher dimensional manifolds; and from smooth structures to metric spaces, weighted manifolds and complexes, and to images, meshes and networks. The first part of the book is a differential geometric study of curves and surfaces in the Euclidean space, enhanced while the second part deals with higher dimensional manifolds centering on curvature by exploring the various ways of extending it to higher dimensional objects and more general structures and how to return to lower dimensional constructs. The third part focuses on computational algorithms in algebraic topology and conformal geomet
£52.00
Cambridge University Press Bäcklund and Darboux Transformations
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£51.29
Cambridge University Press Affine Differential Geometry Geometry of Affine Immersions 111 Cambridge Tracts in Mathematics Series Number 111
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£49.39
Cambridge University Press Comparison Geometry
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£51.29
Cambridge University Press Normal Forms and Bifurcation of Planar Vector Fields
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£49.39
Cambridge University Press Symplectic Fibrations and Multiplicity Diagrams
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£39.89
Cambridge University Press Lectures on Minimal Surfaces Volume 1 Volume 1 Introduction Fundamentals Geometry and Basic Boundary Value Problems
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£50.12
Cambridge University Press A Sampler of RiemannFinsler Geometry 50 Mathematical Sciences Research Institute Publications Series Number 50
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£45.59
Cambridge University Press Tight and Taut Submanifolds 32 Mathematical Sciences Research Institute Publications Series Number 32
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£39.89
Cambridge University Press Differential Geometry and Lie Groups for Physicists
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£61.74
Cambridge University Press The Geometrical Language of Continuum Mechanics
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£78.85
Cambridge University Press Applicable Differential Geometry 0059 London Mathematical Society Lecture Note Series Series Number 59
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£87.39
Cambridge University Press Applied Differential Geometry
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£68.39
Cambridge University Press Algebraic Topology via Differential Geometry 99 London Mathematical Society Lecture Note Series Series Number 99
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£50.99
Cambridge University Press LMSST 11 Spacetime Singularities An Introduction London Mathematical Society Student Texts Series Number 11
Book SynopsisThis book is an elementary introduction to the geometrical methods and notions used in special and general relativity. Particular emphasis is placed on the ideas concerned with the structure of spacetime and those which play a role in the Penrose–Hawking singularity theorems.Trade Review"...fills a need to introduce the singularity theorems, their concepts and techniques to seniors or beginning graduate students." Physics in CanadaTable of ContentsPreface; 1. The geometry of Minkowski spacetime; 2. Some concepts from relativistic mechanics; 3. More general spacetimes: gravity; 4. The proof of Hawking's theorem; References; Index.
£42.74
Cambridge University Press Twistors in Mathematics and Physics
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£53.99
Cambridge University Press Affine Differential Geometry Geometry of Affine Immersions 111 Cambridge Tracts in Mathematics Series Number 111
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£105.45
Cambridge University Press The Geometry of Total Curvature on Complete Open Surfaces 159 Cambridge Tracts in Mathematics Series Number 159
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£105.45
Cambridge University Press An Introduction to Twistor Theory Second Edition 4 London Mathematical Society Student Texts Series Number 4
Book SynopsisThis book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level. The choice of material presented has evolved from graduate lectures given in London and Oxford and the authors have aimed to retain the informal tone of those lectures. The book will provide graduate students with an introduction to the literature of twistor theory, presupposing some knowledge of special relativity and differential geometry. It would also be of use for a short course on space-time structure independently of twistor theory. The physicist could be introduced gently to some of the mathematics which has proved useful in these areas, and the mathematician could be shown where sheaf cohomology and complex manifold theory can be used in physics.Trade Review' … the book is recommended to anyone seeking to get acquainted with the area.' American Scientist' … a certain amount of preliminary knowledge is assumed of the reader ... but anyone who has these prerequisites and who is interested in twistor theory could hardly do better than to start with this book.' Contemporary Physics'In all, the book provides a pleasant starting point for the study of this fascinating subject.' Dr F. E. Burstall, Contemporary PhysicsTable of Contents1. Introduction; 2. Review of tensor algebra; 3. Lorentzian spinors at a point; 4. Spinor fields; 5. Compactified Minkowski space; 6. The geometry of null congruences; 7. The geometry of twistor space; 8. Solving the zero rest mass equations I; 9. Sheaf cohomology; 10. Solving the zero rest mass equations II; 11. The twisted photon and Yang–Mills constructions; 12. The non-linear graviton; 13. Penrose's quasi-local momentum; 14. Cohomological functionals; 15. Further developments and conclusion; Appendix: The GHP equations.
£127.30
Cambridge University Press Singularities 201 London Mathematical Society Lecture Note Series Series Number 201
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£61.71
Cambridge University Press Abelian Functions
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£82.64
Cambridge University Press Introduction to Mbius Differential Geometry 300 London Mathematical Society Lecture Note Series Series Number 300
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£74.13
Cambridge University Press A Primer of Algebraic DModules 33 London Mathematical Society Student Texts Series Number 33
Book SynopsisThe theory of D-modules is a rich area of study combining ideas from algebra and differential equations, and it has significant applications to diverse areas such as singularity theory and representation theory. This book introduces D-modules and their applications avoiding all unnecessary over-sophistication. It is aimed at beginning graduate students and the approach taken is algebraic, concentrating on the role of the Weyl algebra. Very few prerequisites are assumed, and the book is virtually self-contained. Exercises are included at the end of each chapter and the reader is given ample references to the more advanced literature. This is an excellent introduction to D-modules for all who are new to this area.Trade Review'I truly recommend this book, both for its mathematical content and for its light reading.' Bulletin of the London Mathematic Society'A readable account.' MathematikaTable of Contents1. The Weyl algebra; 2. Ideal structure of the Weyl algebra; 3. Rings of differential operators; 4. Jacobian conjectures; 5. Modules over the Weyl algebra; 6. Differential equations; 7. Graded and filtered modules; 8. Noetherian rings and modules; 9. Dimension and multiplicity; 10. Holonomic modules; 11. Characteristic varieties; 12. Tensor products; 13. External products; 14. Inverse image; 15. Embeddings; 16. Direct images; 17. Kashiwara's theorem; 18. Preservation of holonomy; 19. Stability of differential equations; 20. Automatic proof of identities.
£116.85
Cambridge University Press A Primer of Algebraic DModules 33 London Mathematical Society Student Texts Series Number 33
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£42.74
Cambridge University Press Spinning Tops
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£87.39
Cambridge University Press Contact and Symplectic Geometry
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£105.45
Cambridge University Press From Calculus to Cohomology De Rham Cohomology and Characteristic Classes
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£44.99
Cambridge University Press Comparison Geometry
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£105.45
Cambridge University Press Tight and Taut Submanifolds
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£122.55
Cambridge University Press Mixed Hodge Structures and Singularities 132 Cambridge Tracts in Mathematics Series Number 132
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£105.45
Cambridge University Press Geometric Analysis and Lie Theory in Mathematics and Physics 11 Australian Mathematical Society Lecture Series Series Number 11
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£56.74
Cambridge University Press Elementary Geometry of Algebraic Curves
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£104.50
Cambridge University Press Singularity Theory Proceedings of the European Singularities Conference August 1996 Liverpool and Dedicated to CTC Wall on the Occasion of his Lecture Note Series Series Number 263
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£61.71
Cambridge University Press LMS 257 Intro to Noncomm Diff Geom London Mathematical Society Lecture Note Series Series Number 257
This thoroughly revised second edition includes new material on reality conditions and linear connections plus examples from Jordanian deformations and quantum Euclidean spaces. Assuming only some familiarity with ordinary differential geometry and the theory of fibre bundles, this book is accessible to graduate students and newcomers to this field.
£68.33
Cambridge University Press Geometric Partial Differential Equations and Image Analysis
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£46.54
Cambridge University Press Synthetic Differential Geometry 333 London Mathematical Society Lecture Note Series Series Number 333
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£71.65
Cambridge University Press Lectures on Khler Geometry 69 London Mathematical Society Student Texts Series Number 69
Book SynopsisKÃhler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. KÃhler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous KÃhler identities. The final part of the text studies several aspects of compact KÃhler manifolds: the Calabi conjecture, WeitzenbÃck techniques, CalabiâYau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory.Trade Review"A concise and well-written modern introduction to the subject." Tatyana E. Foth, Mathematical ReviewsTable of ContentsIntroduction; Part I. Basics on Differential Geometry: 1. Smooth manifolds; 2. Tensor fields on smooth manifolds; 3. The exterior derivative; 4. Principal and vector bundles; 5. Connections; 6. Riemannian manifolds; Part II. Complex and Hermitian Geometry: 7. Complex structures and holomorphic maps; 8. Holomorphic forms and vector fields; 9. Complex and holomorphic vector bundles; 10. Hermitian bundles; 11. Hermitian and Kähler metrics; 12. The curvature tensor of Kähler manifolds; 13. Examples of Kähler metrics; 14. Natural operators on Riemannian and Kähler manifolds; 15. Hodge and Dolbeault theory; Part III. Topics on Compact Kähler Manifolds: 16. Chern classes; 17. The Ricci form of Kähler manifolds; 18. The Calabi–Yau theorem; 19. Kähler–Einstein metrics; 20. Weitzenböck techniques; 21. The Hirzebruch–Riemann–Roch formula; 22. Further vanishing results; 23. Ricci–flat Kähler metrics; 24. Explicit examples of Calabi–Yau manifolds; Bibliography; Index.
£38.94
Cambridge University Press Curved Spaces From Classical Geometries to Elementary Differential Geometry
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£38.94
Cambridge University Press Elementary Differential Geometry
Book SynopsisThis easy-to-read, generously illustrated textbook is an elementary introduction to differential geometry with emphasis on geometric results, preparing students for more advanced study. Clearly developed arguments and proofs, colour illustrations, and over 100 exercises and solutions make this book ideal for courses and self-study.Trade Review'The book under review presents a detailed and pedagogically excellent study about differential geometry of curves and surfaces by introducing modern concepts and techniques so that it can serve as a transition book between classical differential geometry and contemporary theory of manifolds. the concepts are discussed through historical problems as well as motivating examples and applications. Moreover, constructive examples are given in such a way that the reader can easily develop some understanding for extensions, generalizations and adaptations of classical differential geometry to global differential geometry.' Zentralblatt MATHTable of ContentsPreface; Notation; 1. Euclidean geometry; 2. Curve theory; 3. Classical surface theory; 4. The inner geometry of surfaces; 5. Geometry and analysis; 6. Geometry and topology; 7. Hints for solutions to (most) exercises; Formulary; List of symbols; References; Index.
£47.49
Cambridge University Press Geometry of Riemann Surfaces Proceedings of the Anogia Conference to Celebrate the 65th Birthday of William J Harvey 368 London Mathematical Society Lecture Note Series Series Number 368
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£55.91
Cambridge University Press Spinning Tops A Course on Integrable Systems 51 Cambridge Studies in Advanced Mathematics Series Number 51
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£48.44
Cambridge University Press Bäcklund and Darboux Transformations
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£125.40
Cambridge University Press Contact Geometry and Nonlinear Differential Equations 101 Encyclopedia of Mathematics and its Applications Series Number 101
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£128.25
