Riemannian geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Japanese |
| Published: |
Providence, Rhode Island
American Mathematical Soc.
1996
|
| Series: | Translations of mathematical monographs
149 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Japan. übers. |
| Physical Description: | XIII, 358 S. graph. Darst. |
| ISBN: | 9780821802847 0821802844 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents Preface to the English Edition ix Preface xi Chapter I. Preliminaries fromManifolds 1. Vector Spaces 2. Manifolds 3. Vector Bundles and Linear Connection Problems for Chapter I Notes on the References 1 1 5 15 19 20 Chapter II. Fundamental Conceptsin Riemannian Geometry 1. Riemannian Metric 2. Geodesics 3. Curvature 4. From the Point of View of the Tangent Bundle 5. Riemannian Measure 6. Riemannian Submersion and Complex Projective Space Problems for Chapter II Notes on the References 23 23 32 40 53 61 74 77 80 Chapter III. Global Conceptsin Riemannian Geometry 1. Complete Riemannian Manifolds 2. Variation Formulas and Jacobi Fields 3. Approximation by Finite Dimensional Manifolds and the Index Theorem 4. Cut Locus 5. Ambrose’s Theorem 6. Isometry Group and Holonomy Group Problems for Chapter III Notes on the References 83 83 87 Chapter IV. Comparison Theorems and Applications 1. Spaces of Constant Curvature 2. Comparison Theorems for Jacobi Fields 3. Applications of Comparison Theorems 4. Toponogov’s Comparison Theorem 5. Convexity 6. Symmetric Spaces Problems for Chapter IV vii 97 102 112 117 130 132 135 135 143 154 161 168 175 189
CONTENTS viii Notes on the References 190 Chapter V. Curvature and Topology of Riemannian Manifolds 1. Curvature and Fundamental Group 2. Compact Manifolds of Positive Curvature 3. Open Manifolds of Nonnegative Curvature 4. Manifolds of Nonpositive Curvature Problems for Chapter V Notes on the References 193 193 201 211 221 237 239 Chapter VI. Isoperimetric Inequality and Spectral Geometry 1. The Isoperimetric Inequality 2. The Berger Isoembolic Inequality 3. Eigenvalue Problem for the Laplacian 4. Curvature and Spectrum 5. Heat Kernel and Spectral Geometry Problems for Chapter VI Notes on the References 241 241 252 262 275 282 286 287 Appendices 1. Irreducible Decomposition of the Curvature Tensor 2. Homogeneous Spaces 3. Injectivity Radius Estimate arid ClosedGeodesics 4. Maximum Principle 5. Differential Forms 6. Gromov’s Convergence Theorem and Collapsing of Riemannian Manifolds 289 289 291 294 300 301 Hints and Solutions to Exercises and Problems Chapter I Problems for Chapter I Chapter II Problems for Chapter II Chapter III Problems for Chapter III Chapter IV Problems for Chapter IV Chapter V Problems for Chapter V Chapter VI Problems for Chapter VI 323 323 323 324 326 328 329 331 332 333 333 335 336 Bibliography 339 Index 353 304
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| dewey-sort | 3516.3 273 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV010923985 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:01:11Z |
| institution | BVB |
| isbn | 9780821802847 0821802844 |
| language | English Japanese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007307219 |
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| physical | XIII, 358 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | American Mathematical Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Sakai, Takashi 1941- Verfasser (DE-588)142307122 aut Rīman-kikagaku Riemannian geometry Takashi Sakai Providence, Rhode Island American Mathematical Soc. 1996 XIII, 358 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 149 Aus dem Japan. übers. Riemann, géométrie de ram Geometry, Riemannian Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 s DE-604 Translations of mathematical monographs 149 (DE-604)BV000002394 149 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007307219&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sakai, Takashi 1941- Riemannian geometry Translations of mathematical monographs Riemann, géométrie de ram Geometry, Riemannian Riemannsche Geometrie (DE-588)4128462-8 gnd |
| subject_GND | (DE-588)4128462-8 |
| title | Riemannian geometry |
| title_alt | Rīman-kikagaku |
| title_auth | Riemannian geometry |
| title_exact_search | Riemannian geometry |
| title_full | Riemannian geometry Takashi Sakai |
| title_fullStr | Riemannian geometry Takashi Sakai |
| title_full_unstemmed | Riemannian geometry Takashi Sakai |
| title_short | Riemannian geometry |
| title_sort | riemannian geometry |
| topic | Riemann, géométrie de ram Geometry, Riemannian Riemannsche Geometrie (DE-588)4128462-8 gnd |
| topic_facet | Riemann, géométrie de Geometry, Riemannian Riemannsche Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007307219&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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