Differential geometry of spray and Finsler spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
2001
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 258 S. graph. Darst. |
| ISBN: | 0792368681 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | DIFFERENTIAL GEOMETRY OF SPRAY AND FINSLER SPACES BY ZHONGMIN SHEN
DEPARTMENT OF MATHEMATICAL SCIENCES, INDIANA UNIVERSITY-PURDUE
UNIVERSITY AT INDIANAPOLIS, INDIANAPOLIS, IN, U.S.A. KLUWER ACADEMIC
PUBLISHERS DORDRECHT / BOSTON / LONDON CONTENTS INTRODUCTION 1 1
MINKOWSKI SPACES 3 1.1 MINKOWSKI FUNCTIONALS 4 1.2 CARTAN TORSION 11 1.3
VARGA EQUATION 18 2 FINSLER SPACES 21 2.1 FINSLER METRICS 21 2.2
SPHERICAL METRICS 30 2.3 HYPERBOLIC METRICS 32 3 SODES AND VARIATIONAL
PROBLEMS 35 3.1 SODES 35 3.2 VARIATIONAL PROBLEMS 40 3.3 RELATIONSHIP
BETWEEN EULER-LAGRANGE EQUATIONS 43 4 SPRAY SPACES 47 4.1 SPRAYS 47 4.2
FINSLER SPRAYS 55 4.3 GEODESIES OF FUNK METRICS 59 5 S-CURVATURE 63 5.1
VOLUMES 63 5.2 S-CURVATURE 68 5.3 GEODESIC FLOWS 74 6 NON-RIEMANNIAN
QUANTITIES 77 6.1 BERWALD CURVATURE OF SPRAYS 77 6.2 LANDSBERG CURVATURE
OF FINSLER METRICS 84 6.3 FINSLER SURFACES 89 7 CONNECTIONS 95 7.1
BERWALD CONNECTION OF SPRAYS 95 7.2 CHERN CONNECTION OF FINSLER METRICS
99 7.3 COVARIANT DERIVATIVES ALONG GEODESIES 101 VI CONTENTS 8 RIEMANN
CURVATURE 107 8.1 RIEMANN CURVATURE OF SPRAYS 107 8.2 RIEMANN CURVATURE
OF FINSLER METRICS 117 8.3 RIEMANN CURVATURE OF RIEMANNIAN METRICS 126
8.4 GEODESIC FIELDS AND RIEMANN CURVATURE 129 8.5 VARIATIONAL FORMULAS
131 9 STRUCTURE EQUATIONS OF SPRAYS 133 9.1 BERWALD CONNECTION FORMS 133
9.2 CURVATURE FORMS AND BIANCHI IDENTITIES 135 9.3 R-QUADRATIC AND
R-FLAT SPRAYS 137 10 STRUCTURE EQUATIONS OF FINSLER METRICS 143 10.1
RICCI IDENTITIES FOR G 143 10.2 RICCI IDENTITIES FOR C AND L 147 10.3
R-QUADRATIC AND R-FLAT FINSLER METRICS 148 11 FINSLER SPACES OF SCALAR
CURVATURE 153 11.1 FINSLER METRIC OF SCALAR CURVATURES 153 11.2 FINSLER
METRICS OF CONSTANT CURVATURE 160 11.3 RIEMANNIAN SPACES OF CONSTANT
CURVATURE 167 12 PROJECTIVE GEOMETRY 173 12.1 PROJECTIVELY RELATED
SPRAYS 173 12.2 PROJECTIVELY RELATED FINSLER METRICS 180 12.3
PROJECTIVELY RELATED EINSTEIN METRICS 186 12.4 INVERSE PROBLEMS 190 13
DOUGLAS CURVATURE AND WEYL CURVATURE 197 13.1 DOUGLAS CURVATURE OF
SPRAYS 197 13.2 PROJECTIVELY AFFINE SPRAYS AND DOUGLAS METRICS 199 13.3
WEYL CURVATURE OF SPRAYS 204 13.4 ISOTROPIC SPRAYS AND FINSLER METRICS
OF SCALAR CURVATURE 205 13.5 PROJECTIVELY FLAT SPRAYS AND FINSLER
METRICS 207 13.6 BERWALD-WEYL CURVATURE 212 14 EXPONENTIAL MAPS 221 14.1
EXPONENTIAL MAP OF SPRAYS 221 14.2 JACOBI FIELDS IN SPRAY SPACES 225
14.3 COMPARISON THEOREMS FOR FINSLER SPACES 228 14.4 JACOBI FIELDS IN
ISOTROPIC SPRAY SPACES 231 14.5 FINSLER SPACES OF CONSTANT CURVATURE 238
BIBLIOGRAPHY 243 INDEX 255
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| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
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| id | DE-604.BV013921874 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:54:27Z |
| institution | BVB |
| isbn | 0792368681 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009526089 |
| oclc_num | 248226649 |
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| owner_facet | DE-703 DE-11 |
| physical | VI, 258 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Kluwer |
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| spelling | Shen, Zhongmin Verfasser aut Differential geometry of spray and Finsler spaces by Zhongmin Shen Dordrecht [u.a.] Kluwer 2001 VI, 258 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Finsler spaces Geometry, Differential Sprays (Mathematics) Finsler-Raum (DE-588)4154449-3 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Finsler-Raum (DE-588)4154449-3 s Differentialgeometrie (DE-588)4012248-7 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009526089&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shen, Zhongmin Differential geometry of spray and Finsler spaces Finsler spaces Geometry, Differential Sprays (Mathematics) Finsler-Raum (DE-588)4154449-3 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4154449-3 (DE-588)4012248-7 |
| title | Differential geometry of spray and Finsler spaces |
| title_auth | Differential geometry of spray and Finsler spaces |
| title_exact_search | Differential geometry of spray and Finsler spaces |
| title_full | Differential geometry of spray and Finsler spaces by Zhongmin Shen |
| title_fullStr | Differential geometry of spray and Finsler spaces by Zhongmin Shen |
| title_full_unstemmed | Differential geometry of spray and Finsler spaces by Zhongmin Shen |
| title_short | Differential geometry of spray and Finsler spaces |
| title_sort | differential geometry of spray and finsler spaces |
| topic | Finsler spaces Geometry, Differential Sprays (Mathematics) Finsler-Raum (DE-588)4154449-3 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Finsler spaces Geometry, Differential Sprays (Mathematics) Finsler-Raum Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009526089&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT shenzhongmin differentialgeometryofsprayandfinslerspaces |