Lectures on Finsler geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2001
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 307 S. Ill. |
| ISBN: | 9810245300 9810245319 |
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Record in the Search Index
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| adam_text | LECTURES ON EEVSLER GEOMETRY ZHONGMIN SHEN INDIANA UNIVERSITY-PURDUE
UNIVERSITY INDIANAPODIS, USA WORLD SCIENTIFIC SINGAPORE * NEW JERSEY *
LONDON * HONG KONG CONTENTS PREFACE VII CHAPTER 1 FINSLER SPACES 1 1.1
METRIC SPACES 1 1.2 MINKOWSKI SPACES 6 1.3 FINSLER SPACES 12 CHAPTER 2
FINSLER M SPACES 19 2.1 MEASURE SPACES 19 2.2 VOLUME ON A FINSLER SPACE
21 2.3 HYPERPLANES IN A MINKOWSKI M SPACE 27 2.4 HYPERSURFACES IN A
FINSLER M SPACE 30 CHAPTER 3 CO-AREA FORMULA 35 3.1 LEGENDRE
TRANSFORMATIONS 35 3.2 GRADIENTS OF FUNCTIONS 41 3.3 CO-AREA FORMULA 46
CHAPTER 4 ISOPERIRNETRIC INEQUALITIES 55 4.1 ISOPERIMETRIC PROFILES 56
4.2 SOBOLEV CONSTANTS AND FIRST EIGENVALUE 58 4.3 CONCENTRATION OF
FINSLER M SPACES 64 4.4 OBSERVABLE DIAMETER 69 CHAPTER 5 GEODESIES AND
CONNECTION 75 5.1 GEODESIES 75 XII CONTENTS 5.2 CHERN CONNECTION 80 5.3
COVARIANT DERIVATIVES 88 5.4 GEODESIC FLOW 90 CHAPTER 6 RIEMANN
CURVATURE 95 6.1 BIRTH OF THE RIEMANN CURVATURE 95 6.2 GEODESIC FIELDS
99 6.3 PROJECTIVELY RELATED FINSLER METRICS 101 CHAPTER 7 NON-RIEMANNIAN
CURVATURES 107 7.1 CARTAN TORSION 107 7.2 CHERN CURVATURE 112 7.3
S-CURVATURE 117 CHAPTER 8 STRUCTURE EQUATIONS 125 8.1 STRUCTURE
EQUATIONS OF FINSLER SPACES 125 8.2 STRUCTURE EQUATIONS OF RIEMANNIAN
METRICS 130 8.3 RIEMANN CURVATURE OF RANDERS METRICS 134 CHAPTER 9
FINSLER SPACES OF CONSTANT CURVATURE 137 9.1 FINSLER METRICS OF CONSTANT
CURVATURE 137 9.2 EXAMPLES 141 9.3 RANDERS METRICS OF CONSTANT CURVATURE
145 CHAPTER 10 SECOND VARIATION FORMULA 153 10.1 T-CURVATURE 153 10.2
SECOND VARIATION OF LENGTH 156 10.3 SYNGE THEOREM 162 CHAPTER 11
GEODESIES AND EXPONENTIAL MAP 165 11.1 EXPONENTIAL MAP 165 11.2 JACOBI
FIELDS 167 11.3 MINIMALITY OF GEODESIES 171 11.4 COMPLETENESS OF FINSLER
SPACES 175 CHAPTER 12 CONJUGATE RADIUS AND INJECTIVITY RADIUS 179 12.1
CONJUGATE RADIUS 179 12.2 INJECTIVITY RADIUS 183 12.3 GEODESIC LOOPS AND
CLOSED GEODESIES 189 CONTENTS XIII CHAPTER 13 BASIC COMPARISON THEOREMS
193 13.1 FLAG CURVATURE BOUNDED ABOVE 193 13.2 POSITIVE FLAG CURVATURE
198 13.3 RICCI CURVATURE BOUNDED BELOW 201 13.4 GREEN-DAZORD THEOREM 203
CHAPTER 14 GEOMETRY OF HYPERSURFACES 207 14.1 HESSIAN AND LAPLACIAN 207
14.2 NORMAL CURVATURE 213 14.3 MEAN CURVATURE 218 14.4 SHAPE OPERATOR
221 CHAPTER 15 GEOMETRY OF METRIC SPHERES 229 15.1 ESTIMATES ON THE
NORMAL CURVATURE 229 15.2 CONVEXITY OF METRIC BALLS 234 15.3 ESTIMATES
ON THE MEAN CURVATURE 236 15.4 METRIC SPHERES IN A CONVEX DOMAIN 241
CHAPTER 16 VOLUME COMPARISON THEOREMS 245 16.1 VOLUME OF METRIC BALLS
245 16.2 VOLUME OF TUBULAR NEIGHBORHOODS 252 16.3 GROMOV SIMPLICIAL
NORMS 256 16.4 ESTIMATES ON THE EXPANSION DISTANCE 259 CHAPTER 17 MORSE
THEORY OF LOOP SPACES 265 17.1 A REVIEW ON THE MORSE THEORY 265 17.2
INDEXES OF GEODESIC LOOPS 268 17.3 ENERGY FUNCTIONAL ON A LOOP SPACE 271
17.4 APPROXIMATION OF LOOP SPACES 273 CHAPTER 18 VANISHING THEOREMS FOR
HOMOTOPY GROUPS 279 18.1 INTERMEDIATE CURVATURES 279 18.2 VANISHING
THEOREM FOR HOMOTOPY GROUPS 280 18.3 FINSLER SPACES OF POSITIVE CONSTANT
CURVATURE 286 CHAPTER 19 SPACES OF FINSLER SPACES 291 19.1
GROMOV-HAUSDORFF DISTANCE 291 19.2 PRECOMPACTNESS THEOREM 293
|
| any_adam_object | 1 |
| author | Shen, Zhongmin |
| author_facet | Shen, Zhongmin |
| author_role | aut |
| author_sort | Shen, Zhongmin |
| author_variant | z s zs |
| building | Verbundindex |
| bvnumber | BV017379370 |
| callnumber-first | Q - Science |
| callnumber-label | QA689 |
| callnumber-raw | QA689 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)47797302 (DE-599)BVBBV017379370 |
| dewey-full | 516.3/73 516.375 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/73 516.375 |
| dewey-search | 516.3/73 516.375 |
| dewey-sort | 3516.3 273 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV017379370 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:17:18Z |
| institution | BVB |
| isbn | 9810245300 9810245319 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010472781 |
| oclc_num | 47797302 |
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| owner_facet | DE-355 DE-BY-UBR DE-20 DE-11 |
| physical | XIV, 307 S. Ill. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Shen, Zhongmin Verfasser aut Lectures on Finsler geometry Zhongmin Shen Singapore [u.a.] World Scientific 2001 XIV, 307 S. Ill. txt rdacontent n rdamedia nc rdacarrier Espaços de finsler larpcal Finsler, Espaces de Geometria diferencial larpcal Géométrie différentielle Finsler spaces Geometry, Differential Finsler-Raum (DE-588)4154449-3 gnd rswk-swf Finsler-Raum (DE-588)4154449-3 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010472781&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shen, Zhongmin Lectures on Finsler geometry Espaços de finsler larpcal Finsler, Espaces de Geometria diferencial larpcal Géométrie différentielle Finsler spaces Geometry, Differential Finsler-Raum (DE-588)4154449-3 gnd |
| subject_GND | (DE-588)4154449-3 |
| title | Lectures on Finsler geometry |
| title_auth | Lectures on Finsler geometry |
| title_exact_search | Lectures on Finsler geometry |
| title_full | Lectures on Finsler geometry Zhongmin Shen |
| title_fullStr | Lectures on Finsler geometry Zhongmin Shen |
| title_full_unstemmed | Lectures on Finsler geometry Zhongmin Shen |
| title_short | Lectures on Finsler geometry |
| title_sort | lectures on finsler geometry |
| topic | Espaços de finsler larpcal Finsler, Espaces de Geometria diferencial larpcal Géométrie différentielle Finsler spaces Geometry, Differential Finsler-Raum (DE-588)4154449-3 gnd |
| topic_facet | Espaços de finsler Finsler, Espaces de Geometria diferencial Géométrie différentielle Finsler spaces Geometry, Differential Finsler-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010472781&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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