Lectures on differential geometry:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2000
|
| Edition: | Reprint. |
| Series: | Series on university mathematics
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 356 S. graph. Darst. |
| ISBN: | 9810234945 9810241828 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804128294191235072 |
|---|---|
| adam_text | Contents
1 Differentiable Manifolds 1
§1-1 Definition of Differentiable Manifolds 1
§1-2 Tangent Spaces 9
§1-3 Submanifolds 18
§1-4 Frobenius Theorem 29
2 Multilinear Algebra 39
§2-1 Tensor Products 39
§2-2 Tensors 47
§2-3 Exterior Algebra 52
3 Exterior Differential Calculus 65
§3-1 Tensor Bundles and Vector Bundles 65
§3-2 Exterior Differentiation 74
§3-3 Integrals of Differential Forms 85
§3-4 Stokes Formula 92
4 Connections 101
§4-1 Connections on Vector Bundles 101
§4-2 Affine Connections 113
§4-3 Connections on Frame Bundles 121
5 Riemannian Geometry 133
§5-1 The Fundamental Theorem of Riemannian Geometry 133
§5-2 Geodesic Normal Coordinates 143
§5-3 Sectional Curvature 155
§5-4 The Gauss-Bonnet Theorem 162
6 Lie Groups and Moving Frames 173
§6-1 Lie Groups 173
§6-2 Lie Transformation Groups 186
§6-3 The Method of Moving Frames 198
ix
x CONTENTS
§6-4 Theory of Surfaces 210
7 Complex Manifolds 221
§7-1 Complex Manifolds 221
§7-2 The Complex Structure on a Vector Space 227
§7-3 Almost Complex Manifolds 236
§7-4 Connections on Complex Vector Bundles 244
§7-5 Hermitian Manifolds and Kahlerian Manifolds 256
8 Finsler Geometry 265
§8-1 Preliminaries 265
§8-2 Geometry on the Projectivised Tangent Bundle (PTM) and the
Hilbert Form 267
§8-3 The Chern Connection 273
§8-3.1 Determination of the Connection 274
§8-3.2 The Cartan Tensor and Characterization of Riemannian
Geometry 280
§8-3.3 Explicit Formulas for the Connection Forms in Natural
Coordinates 283
§8-4 Structure Equations and the Flag Curvature 288
§8-4.1 The Curvature Tensor 289
§8-4.2 The Flag Curvature and the Ricci Curvature 293
§8-4.3 Special Finsler Spaces 295
§8-5 The First Variation of Arc Length and Geodesies 297
§8-6 The Second Variation of Arc Length and Jacobi Fields 306
§8-7 Completeness and the Hopf-Rinow Theorem 314
§8-8 The Theorems of Bonnet-Myers and Synge 325
A Historical Notes 331
§A-l Classical Differential Geometry 331
§A-2 Riemannian Geometry 331
§A-3Manifolds 332
§A-4Global Geometry 332
B Differential Geometry and Theoretical Physics 335
§B-1 Dynamics and Moving Frames 336
§B-2 Theory of Surfaces, Solitons and the Sigma Model 338
§B-3Gauge Field Theory 340
§B-4 Conclusion 341
References 343
Index 347
|
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| discipline | Mathematik |
| edition | Reprint. |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:46:57Z |
| institution | BVB |
| isbn | 9810234945 9810241828 |
| language | English |
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| physical | X, 356 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
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| spelling | Chern, Shiing-shen 1911-2004 Verfasser (DE-588)118520350 aut Lectures on differential geometry S. S. Chern ; W. H. Chen ; K. S. Lam Reprint. Singapore [u.a.] World Scientific 2000 X, 356 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series on university mathematics 1 Differentialgeometrie Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s DE-604 Chen, Wei-huan Verfasser aut Lam, Kai Shue Verfasser aut Series on university mathematics 1 (DE-604)BV008161912 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009217013&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chern, Shiing-shen 1911-2004 Chen, Wei-huan Lam, Kai Shue Lectures on differential geometry Series on university mathematics Differentialgeometrie Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4012248-7 |
| title | Lectures on differential geometry |
| title_auth | Lectures on differential geometry |
| title_exact_search | Lectures on differential geometry |
| title_full | Lectures on differential geometry S. S. Chern ; W. H. Chen ; K. S. Lam |
| title_fullStr | Lectures on differential geometry S. S. Chern ; W. H. Chen ; K. S. Lam |
| title_full_unstemmed | Lectures on differential geometry S. S. Chern ; W. H. Chen ; K. S. Lam |
| title_short | Lectures on differential geometry |
| title_sort | lectures on differential geometry |
| topic | Differentialgeometrie Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009217013&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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