DIFFERENTIAL GEOMETRY AND SYMMETRIC SPACESpdf电子书版本下载

点此进入-本书在线PDF格式电子书下载【推荐-云解压-方便快捷】直接下载PDF格式图书。移动端-PC端通用
种子下载[BT下载速度快] 温馨提示：（请使用BT下载软件FDM进行下载）软件下载地址页 直链下载[便捷但速度慢]   [在线试读本书]   [在线获取解压码]

DIFFERENTIAL GEOMETRY AND SYMMETRIC SPACESPDF格式电子书版下载

下载的文件为RAR压缩包。需要使用解压软件进行解压得到PDF格式图书。

建议使用BT下载工具Free Download Manager进行下载,简称FDM(免费,没有广告,支持多平台）。本站资源全部打包为BT种子。所以需要使用专业的BT下载软件进行下载。如 BitComet qBittorrent uTorrent等BT下载工具。迅雷目前由于本站不是热门资源。不推荐使用！后期资源热门了。安装了迅雷也可以迅雷进行下载！

（文件页数 要大于 标注页数，上中下等多册电子书除外）

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

CHAPTER Ⅰ Elementary Differential Geometry 1

1．Manifolds 2

2．Tensor Fields 8

1．Vector Fields ard I-Forms 8

2．The Tensor Algebra 13

3．The Grassmann Algebra 17

4．Exterior Differentiation 19

3．Mappings 22

1．The Interpretation of the Jacobian 22

2．Transformation of Vector Fields 24

3．Effect on Differential Forms 25

4．Affine Connections 26

5．Parallelism 28

6．The Exponential Mapping 32

7．Covariant Differentiation 40

8．The Structural Equations 43

9．The Riemannian Connection 47

10．Complete Riemannian Manifolds 55

11．Isometries 60

12．Sectional Curvature 64

13．Riemannian Manifolds of Negative Curvature 70

14．Totally Geodesic Submanifolds 78

Exercises 82

Notes 85

CHAPTER Ⅱ Lie Groups and Lie Algebras 87

1．The Exponential Mapping 88

1．The Lie Algebra of a Lie Group 88

2．The Universal Enveloping Algebra 90

3．Left Invariant Affine Connections 92

4．Taylor＇s Formula and Applications 94

2．Lie Subgroups and Subalgebras 102

3．Lie Transformation Groups 110

4．Coset Spaces and Homogeneous Spaces 113

5．The Adjoint Group 116

6．Semisimple Lie Groups 121

Exercises 125

Notes 128

CHAPTER Ⅲ Structure of Semisimple Lie Algebras 130

1．Preliminaries 130

2．Theorems of Lie and Engel 133

3．Cartan Subalgebras 137

4．Root Space Decomposition 140

5．Significance of the Root Pattern 146

6．Real Forms 152

7．Caftan Decompositions 156

Exercises 160

Notes 161

CHAPTER Ⅳ Symmetric Spaces 162

1．Affine Locally Symmetric Spaces 163

2．Groups of Isometries 166

3．Riemannian Globally Symmetric Spaces 170

4．The Exponential Mapping and the Curvature 179

5．Locally and Globally Symmetric Spaces 183

6．Compact Lie Groups 188

7．Totally Geodesic Submanifolds．Lie Triple Systems 189

Exercises 191

Notes 191

CHAPTER Ⅴ Decomposition of Symmetric Spaces 193

1．Orthogonal Symmetric Lie Algebras 193

2．The Duality 199

3．Sectional Curvature of Symmetric Spaces 205

4．Symmetric Spaces with Semisimple Groups of Isometries 207

5．Notational Conventions 208

6．Rank of Symmetric Spaces 209

Exercises 213

Notes 213

CHAPTER Ⅵ Symmetric Spaces of the Noncompact Type 214

1．Decomposition of a Semisimple Lie Group 214

2．Maximal Compact Subgroups and Their Conjugacy 218

3．The Iwasawa Decomposition 219

4．Nilpotent Lie Groups 225

5．Global Decompositions 234

6．The Complex Case 237

Exercises 239

Notes 240

CHAPTER Ⅶ Symmetric Spaces of the Compact Type 241

1．The Contrast between the Compact Type and the Noncompact Type 241

2．The Weyl Group 243

3．Conjugate Points．Singular Points．The Diagram 250

4．Applications to Compact Groups 254

5．Control over the Singular Set 260

6．The Fundamental Group and the Center 264

7．Application to the Symmetric Space U/K 271

8．Classification of Locally Isometric Spaces 273

9．Appendix．Results from Dimension Theory 275

Exercises 278

Notes 280

CHAPTER Ⅷ Hermitian Symmetric Spaces 281

1．Almost Complex Manifolds 281

2．Complex Tensor Fields．The Ricci Curvature 285

3．Bounded Domains．The Kernel Function 293

4．Hermitian Symmetric Spaces of the Compact Type and the Noncompact Type 301

5．Irreducible Orthogonal Symmetric Lie Algebras 306

6．Irreducible Hermitian Symmetric Spaces 310

7．Bounded Symmetric Domains 311

Exercises 322

Notes 325

CHAPTER Ⅸ On the Classification of Symmetric Spaces 326

1．Reduction of the Problem 326

2．Automorphisms 331

3．Involutive Automorphisms 334

4．E．Cartan＇s List of Irreducible Riemannian Globally Symmetric Spaces 339

1．Some Matrix Groups and Their Lie Algebras 339

2．The Simple Lie Algebras over C and Their Compact Real Forms．The Irreducible Riemannian Globally Symmetric Spaces of Type Ⅱ and Type Ⅳ 346

3．The Involutive Automorphisms of Simple Compact Lie Algebras．The Irreducible Globally Symmetric Spaces of Type Ⅰ and Type Ⅲ 347

4．Irreducible Hermitian Symmetric Spaces 354

5．Two-Point Homogeneous Spaces．Symmetric Spaces of Rank One．Closed Geodesics 355

Exercises 358

Notes 359

CHAPTER Ⅹ Functions on Symmetric Spaces 360

1．Integral Formulas 361

1．Generalities 361

2．Invariant Measures on Coset Spaces 367

3．Some Integral Formulas for Semisimple Lie Groups 372

4．Integral Formulas for the Cartan Decomposition 379

5．The Compact Case 382

2．Invariant Differential Operators 385

1．Generalities．The Laplace-Behrami Operator 385

2．Invariant Differential Operators on Reductive Coset Spaces 389

3．The Case of a Symmetric Space 396

3．Spherical Functions．Definition and Examples 398

4．Elementary Properties of Spherical Functions 408

5．Some Algebraic Tools 518

6．The Formula for the Spherical Function 422

1．The Euclidean Type 422

2．The Compact Type 423

3．The Noncompact Type 427

7．Mean Value Theorems 435

1．The Mean Value Operators 435

2．Approximations by Analytic Functions 440

3．The Darboux Equation in a Symmetric Space 442

4．Poisson＇s Equation in a Two-Point Homogeneous Space 444

Exercises 449

Notes 454

BIBLIOGRAPHY 457

LIST OF NOTATIONAL CONVENTIONS 473

SYMBOLS FREQUENTLY USED 476

AUTHOR INDEX 479

SUBJECT INDEX 482