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黎曼几何和几何分析 第6版PDF|Epub|txt|kindle电子书版本网盘下载
- （德）约斯特（Jurgen Jost）著 著
- 出版社： 北京;西安：世界图书出版公司
- ISBN：9787510084447
- 出版时间：2015
- 标注页数：611页
- 文件大小：69MB
- 文件页数：625页
- 主题词：黎曼几何－研究生－教材－英文；几何－数学分析－研究生－教材－英文
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图书目录
1 Riemannian Manifolds1
1.1 Manifolds and Differentiable Manifolds1
1.2 Tangent Spaces6
1.3 Submanifolds10
1.4 Riemannian Metrics13
1.5 Existence of Geodesics on Compact Manifolds28
1.6 The Heat Flow and the Existence of Geodesics31
1.7 Existence of Geodesics on Complete Manifolds35
Exercises for Chapter 137
2 Lie Groups and Vector Bundles41
2.1 Vector Bundles41
2.2 Integral Curves of Vector Fields.Lie Algebras51
2.3 Lie Groups61
2.4 Spin Structures67
Exercises for Chapter 287
3 The Laplace Operator and Harmonic Differential Forms89
3.1 The Laplace Operator on Functions89
3.2 The Spectrum of the Laplace Operator94
3.3 The Laplace Operator on Forms102
3.4 Representing Cohomology Classes by Harmonic Forms113
3.5 Generalizations122
3.6 The Heat Flow and Harmonic Forms123
Exercises for Chapter 3129
4 Connections and Curvature133
4.1 Connections in Vector Bundles133
4.2 Metric Connections.The Yang-Mills Functional144
4.3 The Levi-Civita Connection160
4.4 Connections for Spin Structures and the Dirac Operator175
4.5 The Bochner Method182
4.6 Eigenvalue Estimates by the Method of Li-Yau187
4.7 The Geometry of Submanifolds191
4.8 Minimal Submanifolds196
Exercises for Chapter 4203
5 Geodesics and Jacobi Fields205
5.1 First and second Variation of Arc Length and Energy205
5.2 Jacobi Fields211
5.3 Conjugate Points and Distance Minimizing Geodesics219
5.4 Riemannian Manifolds of Constant Curvature227
5.5 The Rauch Comparison Theorems and Other Jacobi Field Estimates229
5.6 Geometric Applications of Jacobi Field Estimates234
5.7 Approximate Fundamental Solutions and Representation Formulas239
5.8 The Geometry of Manifolds of Nonpositive Sectional Curvature241
Exercises for Chapter 5258
A Short Survey on Curvature and Topology261
6 Symmetric Spaces and K？hler Manifolds269
6.1 Complex Projective Space269
6.2 K？hler Manifolds275
6.3 The Geometry of Symmetric Spaces285
6.4 Some Results about the Structure of Symmetric Spaces296
6.5 The Space Sl(n,R)/SO(n,R)303
6.6 Symmetric Spaces of Noncompact Type320
Exercises for Chapter 6325
7 Morse Theory and Floer Homology327
7.1 Preliminaries:Aims of Morse Theory327
7.2 The Palais-Smale Condition,Existence of Saddle Points332
7.3 Local Analysis334
7.4 Limits of Trajectories of the Gradient Flow350
7.5 Floer Condition,Transversality and Z2-Cohomology358
7.6 Orientations and Z-homology364
7.7 Homotopies368
7.8 Graph flows372
7.9 Orientations376
7.10 The Morse Inequalities392
7.11 The Palais-Smale Condition and the Existence of Closed Geodesics403
Exercises for Chapter 7416
8 Harmonic Maps between Riemannian Manifolds419
8.1 Definitions419
8.2 Formulas for Harmonic Maps.The Bochner Technique426
8.3 The Energy Integral and Weakly Harmonic Maps438
8.4 Higher Regularity448
8.5 Existence of Harmonic Maps for Nonpositive Curvature459
8.6 Regularity of Harmonic Maps for Nonpositive Curvature466
8.7 Harmonic Map Uniqueness and Applications485
Exercises for Chapter 8492
9 Harmonic Maps from Riemann Surfaces495
9.1 Two-dimensional Harmonic Mappings495
9.2 The Existence of Harmonic Maps in Two Dimensions509
9.3 Regularity Results530
Exercises for Chapter 9544
10 Variational Problems from Quantum Field Theory547
10.1 The Ginzburg-Landau Functional547
10.2 The Seiberg-Witten Functional555
10.3 Dirac-harmonic Maps562
Exercises for Chapter 10569
A Linear Elliptic Partial Differential Equations571
A.1 Sobolev Spaces571
A.2 Linear Elliptic Equations576
A.3 Linear Parabolic Equations580
B Fundamental Groups and Covering Spaces583
Bibliography587
Index605