Riemannian geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
<<de>> Gruyter
1995
|
| Edition: | 2., rev. ed. |
| Series: | De Gruyter studies in mathematics
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 409 S. |
| ISBN: | 3110145936 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Table of Contents
Chapter 1: Foundations
1.0 Review of Differential Calculus and Topology 1
1.1 Differentiable Manifolds 8
1.2 Tensor Bundles 13
1.3 Immersions and Submersions 23
1.4 Vector Fields and Tensor Fields 31
1.5 Covariant Derivation 39
1.6 The Exponential Mapping 53
1.7 Lie Groups 59
1.8 Riemannian Manifolds 67
1.9 Geodesies and Convex Neighborhoods 78
1.10 Isometric Immersions 86
1.11 Riemannian Curvature 97
1.12 Jacobi Fields 109
Chapter 2: Curvature and Topology
2.1 Completeness and Cut Locus 124
2.1 Appendix Orientation 136
2.2 Symmetric Spaces 141
2.3 The Hilbert Manifold of H curves 158
2.4 The Loop Space and the Space of Closed Curves 170
2.5 The Second Order Neighborhood of a Critical Point 181
2.5 Appendix The S1 and the Z2 action on A M 196
2.6 Index and Curvature 203
2.6 Appendix The Injectivity Radius for 1/4 pinched Manifolds 212
2.7 Comparison Theorems for Triangles 215
2.8 The Sphere Theorem 229
2.9 Non compact Manifolds of Positive Curvature 240
Chapter 3: Structure of the Geodesic Flow
3.1 Hamiltonian Systems 256
3.2 Properties of the Geodesic Flow 265
x Table of Contents
3.3 Stable and Unstable Motions 279
3.4 Geodesies on Surfaces 288
3.5 Geodesies on the Ellipsoid 303
3.6 Closed Geodesies on Spheres 324
3.7 The Theorem of the Three Closed Geodesies 337
3.8 Manifolds of Non Positive Curvature 350
3.9 The Geodesic Flow on Manifolds of Negative Curvature 363
3.10 The Main Theorem for Surfaces of Genus 0 380
References 393
Index 403
|
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| discipline | Mathematik |
| edition | 2., rev. ed. |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:46:01Z |
| institution | BVB |
| isbn | 3110145936 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006685035 |
| oclc_num | 440085957 |
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| physical | X, 409 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | <<de>> Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematics |
| series2 | De Gruyter studies in mathematics |
| spelling | Klingenberg, Wilhelm 1924-2010 Verfasser (DE-588)119135884 aut Riemannian geometry Wilhelm P. A. Klingenberg 2., rev. ed. Berlin [u.a.] <<de>> Gruyter 1995 X, 409 S. txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics 1 Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 s DE-604 De Gruyter studies in mathematics 1 (DE-604)BV000005407 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006685035&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Klingenberg, Wilhelm 1924-2010 Riemannian geometry De Gruyter studies in mathematics Riemannsche Geometrie (DE-588)4128462-8 gnd |
| subject_GND | (DE-588)4128462-8 |
| title | Riemannian geometry |
| title_auth | Riemannian geometry |
| title_exact_search | Riemannian geometry |
| title_full | Riemannian geometry Wilhelm P. A. Klingenberg |
| title_fullStr | Riemannian geometry Wilhelm P. A. Klingenberg |
| title_full_unstemmed | Riemannian geometry Wilhelm P. A. Klingenberg |
| title_short | Riemannian geometry |
| title_sort | riemannian geometry |
| topic | Riemannsche Geometrie (DE-588)4128462-8 gnd |
| topic_facet | Riemannsche Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006685035&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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