Foliations on Riemannian manifolds and submanifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Boston ; Basel ; Berlin
Birkhäuser
1998
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 255 - 281 |
| Beschreibung: | X, 286 S. graph. Darst. |
| ISBN: | 3764338067 0817638067 |
Internformat
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| 245 | 1 | 0 | |a Foliations on Riemannian manifolds and submanifolds |c Vladimir Y. Rovenskii |
| 264 | 1 | |a Boston ; Basel ; Berlin |b Birkhäuser |c 1998 | |
| 300 | |a X, 286 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 500 | |a Literaturverz. S. 255 - 281 | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
Preface vii
I. Foliations on Manifolds 1
1.1 Definitions and examples of foliations 1
1.2 Holonomy 13
1.3 Ehresmann foliations 19
1.4 Foliations and curvature 25
II. Local Riemannian Geometry of Foliations 31
2.1 The main tensors and their invariants 31
2.2 A Riemannian almost product structure 36
2.3 Constructions of geodesic and umbilic foliations 40
2.4 Curvature identities 48
2.5 Riemannian foliations 55
HI. T Parallel Fields and Mixed Curvature 64
3.1 Jacobi and Riccati equations 64
3.2 J parallel vector fields and the Jacobi equation 73
3.3 L parallel vector fields and variations of curves 77
3.4 Positive mixed curvature 79
IV. Rigidity and Splitting of Foliations 95
4.1 Foliations on space forms 96
4.2 Area and volume of a J parallel vector field 98
4.3 Riccati and Raychaudhuri equations 116
V. Submanifolds with Generators 129
5.1 Submanifolds with generators in Riemannian spaces ... 129
5.2 Submanifolds with generators in space forms 137
5.3 Submanifolds with nonpositive extrinsic g Ricci curvature . 151
5.4 Ruled submanifolds with conditions on mean curvature . . 164
5.5 Submanifolds with spherical generators 170
vi Contents
VI. Decomposition of Ruled Submanifolds 175
6.1 Cylindricity of submanifolds in a Riemannian space
of nonnegative curvature 176
6.2 Ruled submanifolds in CROSS and the Segre embedding . 183
6.3 Ruled submanifolds in a Riemannian space of positive
curvature and Segre type embeddings 192
VII. Decomposition of Parabolic Submanifolds 201
7.1 Parabolic submanifolds in CROSS 201
7.2 Parabolic submanifolds in a Riemannian space
of positive curvature 211
7.3 Remarks on pseudo Riemannian isometric immersions . . 215
Appendix A. Great Sphere Foliations and Manifolds
with Curvature Bounded Above 218
A.I Great circle foliations 218
A.2 Extremal theorem for manifolds
with curvature bounded above 223
Appendix B. Submersions of Riemannian Manifolds
with Compact Leaves 235
Appendix C. Foliations by Closed Geodesies
with Positive Mixed Sectional Curvature 247
References 255
Index 283
|
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| discipline | Mathematik |
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| id | DE-604.BV011962677 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:19:15Z |
| institution | BVB |
| isbn | 3764338067 0817638067 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008089418 |
| oclc_num | 247092699 |
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| physical | X, 286 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Rovenski, Vladimir 1953- Verfasser (DE-588)12012985X aut Foliations on Riemannian manifolds and submanifolds Vladimir Y. Rovenskii Boston ; Basel ; Berlin Birkhäuser 1998 X, 286 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 255 - 281 Blätterung - Riemannscher Raum Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Blätterung (DE-588)4007006-2 gnd rswk-swf Blätterung (DE-588)4007006-2 s Riemannscher Raum (DE-588)4128295-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008089418&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rovenski, Vladimir 1953- Foliations on Riemannian manifolds and submanifolds Blätterung - Riemannscher Raum Riemannscher Raum (DE-588)4128295-4 gnd Blätterung (DE-588)4007006-2 gnd |
| subject_GND | (DE-588)4128295-4 (DE-588)4007006-2 |
| title | Foliations on Riemannian manifolds and submanifolds |
| title_auth | Foliations on Riemannian manifolds and submanifolds |
| title_exact_search | Foliations on Riemannian manifolds and submanifolds |
| title_full | Foliations on Riemannian manifolds and submanifolds Vladimir Y. Rovenskii |
| title_fullStr | Foliations on Riemannian manifolds and submanifolds Vladimir Y. Rovenskii |
| title_full_unstemmed | Foliations on Riemannian manifolds and submanifolds Vladimir Y. Rovenskii |
| title_short | Foliations on Riemannian manifolds and submanifolds |
| title_sort | foliations on riemannian manifolds and submanifolds |
| topic | Blätterung - Riemannscher Raum Riemannscher Raum (DE-588)4128295-4 gnd Blätterung (DE-588)4007006-2 gnd |
| topic_facet | Blätterung - Riemannscher Raum Riemannscher Raum Blätterung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008089418&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rovenskivladimir foliationsonriemannianmanifoldsandsubmanifolds |