Tangent and cotangent bundles: differential geometry
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Dekker
1973
|
| Schriftenreihe: | Pure and applied mathematics
16 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 423 S. |
| ISBN: | 0824760719 |
Internformat
MARC
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| 100 | 1 | |a Yano, Kentarō |d 1912-1993 |e Verfasser |0 (DE-588)119350262 |4 aut | |
| 245 | 1 | 0 | |a Tangent and cotangent bundles |b differential geometry |c Kentaro Yano ; Shigeru Ishihara |
| 264 | 1 | |a New York |b Dekker |c 1973 | |
| 300 | |a IX, 423 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pure and applied mathematics |v 16 | |
| 650 | 4 | |a Faisceaux tangentiels | |
| 650 | 4 | |a Géométrie différentielle | |
| 650 | 4 | |a Geometry, Differential | |
| 650 | 4 | |a Tangent bundles | |
| 650 | 0 | 7 | |a Tangentialbündel |0 (DE-588)4236004-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kotangentialbündel |0 (DE-588)4403097-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differentialgeometrie |0 (DE-588)4012248-7 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Tangentialbündel |0 (DE-588)4236004-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Kotangentialbündel |0 (DE-588)4403097-6 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Tangentialbündel |0 (DE-588)4236004-3 |D s |
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| 700 | 1 | |a Ishihara, Shigeru |e Verfasser |4 aut | |
| 830 | 0 | |a Pure and applied mathematics |v 16 |w (DE-604)BV000001885 |9 16 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-003571006 | ||
Datensatz im Suchindex
| _version_ | 1804119901847158784 |
|---|---|
| adam_text | CONTENTS
Preface iii
Chapter I VERTICAL AND COMPLETE LIFTS FROM A
MANIFOLD TO ITS TANGENT BUNDLE . . 1
1. The Tangent Bundle 1
2. Vertical Lifts 4
3. Complete Lifts 14
4. Lifts of Derivations 26
5. Complete Lifts of Tensor Fields
of Type (1,1) and of Type (0, 2) ... 33
6. Complete Lifts of Affine Connections . . 40
7. Formulas on Lie Derivatives .... 48
8. Properties of Differentiable Mappings . . 52
9. Geodesies and Parallel Displacements
in a Tangent Bundle 57
10. The Tangent Bundle of a Symmetric Space . 61
11. Complete Lifts of f Structures and
Almost Contact Structures . . . . 63
12. Infinitesimal Affine Transformations in
a Tangent Bundle 67
Exercises 1 ....... 81
Chapter II HORIZONTAL LIFTS FROM A MANIFOLD
TO ITS TANGENT BUNDLE 86
1. Horizontal Lifts of Functions and Vector Fields 86
2. Horizontal Lifts of 1 Forms .... 92
3. Horizontal Lifts of Tensor Fields ... 93
4. Adapted Frames 98
v
vi CONTENTS
5. Horizontal Lifts of Tensor Fields of
Type (1,1) 102
6. Horizontal Lifts of Tensor Fields of
Type (0,2) 105
7. Horizontal Lifts of Affine Connections . . 106
8. Formulas on Lie Derivatives . . . . 113
9. Geodesies and Parallel Displacements
in a Tangent Bundle 114
10. Almost Complex Structures in a Tangent Bundle 117
Exercises 2 120
Chapter III CROSS SECTIONS IN THE TANGENT BUNDLE . 122
1. Lifts of Tensor Fields on a Cross Section . 122
2. Lifts of Tensor Fields of Type (1, 1) and of
Type (0, 2) on a Cross Section . . . 127
3. Affine Connections Induced on a
Cross Section 131
Exercises 3 136
Chapter IV TANGENT BUNDLES OF RIEMANNIAN MANIFOLDS 137
1. Metrics in the Tangent Bundle of a
Riemannian Manifold 137
2. The Metric II in the Tangent Bundle of
a Riemannian Manifold 139
3. The Metric I + II in the Tangent Bundle of
a Riemannian Manifold 147
4. The Metric Connection with Respect
to the Metric II 151
5. The Metric I + III in the Tangent Bundle of
a Riemannian Manifold 155
6. Almost Kahlerian Structures in a Tangent
Bundle with Metric I + III . . . . 166
7. Geodesies in a Tangent Bundle with
Metric I + III 171
Exercises 4 175
CONTENTS vii
Chapter V PROLONGATIONS OF G STRUCTURES
TO TANGENT BUNDLES 178
1. The Tangent Group 178
2. The Prolongation of a G Structure to
the Tangent Bundle 186
3. The Integrability of the Prolongation of
a G Structure 189
4. Prolongations of Tensor Fields and
G Structures to the Tangent Bundle . . 192
5. Lifts of G Connections 197
6. The Linear Holonomy Group in the
Tangent Bundle 204
Exercises 5 207
Chapter VI NON LINEAR CONNECTIONS IN
TANGENT BUNDLES 209
1. Non Linear Connections 209
2. Horizontal Lifts of Vector Fields . . . 214
3. Almost Complex Structures in the
Tangent Bundle 216
4. Finsler Metrics and Non Linear Connections 218
Exercises 6 223
Chapter VII VERTICAL AND COMPLETE LIFTS FROM A
MANIFOLD TO ITS COTANGENT BUNDLE . . 224
1. The Cotangent Bundle 224
2. The Basic 1 Form in the Cotangent Bundle . 226
3. Vertical Lifts of Tensor Fields of Type (0, s) 227
4. Complete Lifts of Vector Fields . . . 234
5. Complete Lifts of Tensor Fields of Type (1, 1)
and of Type (1, 2) 241
6. Complete Lifts of Derivations . . . 246
7. Almost Complex Structures in the
Cotangent Bundle 250
viii CONTENTS
8. f Structures in the Cotangent Bundle . . 259
9. The Cotangent Group 262
10. The Riemann Extension and the Complete Lift
of a Symmetric Affine Connection . . . 268
Exercises 7 274
Chapter VIII HORIZONTAL LIFTS FROM A MANIFOLD TO
ITS COTANGENT BUNDLE 276
1. Horizontal Lifts of Vector Fields . . . 276
2. Horizontal Lifts of Tensor Fields of Type (1, 1) 280
3. Almost Complex Structures and f Structures
in the Cotangent Bundle 283
4. Horizontal Lifts of Affine Connections . . 28 5
5. Adapted Frames and Diagonal Lifts of
Tensor Fields of Type (1, 1) .... 289
6. Geodesies and Parallel Displacements in
a Cotangent Bundle 297
Exercises 8 300
Chapter IX TENSOR FIELDS AND CONNECTIONS ON
CROSS SECTIONS IN THE COTANGENT BUNDLE 301
1. Lifts of Vector Fields on a Cross Section . 301
2. Metrics and Connections Induced on a
Cross Section 304
3. Lifts of Tensor Fields of Type (1, 1) on a
Cross Section 308
Exercises 9 314
Chapter X PROLONGATIONS OF TENSOR FIELDS AND
CONNECTIONS TO THE TANGENT BUNDLE
OF ORDER 2 315
1. The Tangent Bundle of Order 2 . . . 315
2. Lifts of Functions, Vector Fields and 1 Forms 319
3. Lifts of Tensor Fields 325
CONTENTS ix
4. Local Expressions for Lifts of Tensor Fields 330
5. Lifts of Tensor Fields of Type (1, 1) . . 335
6. Lifts of Affine Connections .... 338
7. Lifts of Infinitesimal Transformations . . 344
8. Geodesies and Parallel Displacements in a
Tangent Bundle of Order 2 .... 347
9. The Tangent Group of Order 2 . . . 352
10. Prolongations of G Structures to the
Tangent Bundle of Order 2 .... 358
11. The Linear Holonomy Group in the
Tangent Bundle of Order 2 . . . . 367
Exercises 10 369
Chapter XI PROLONGATIONS OF TENSOR FIELDS, CON¬
NECTIONS AND G STRUCTURES TO THE
TANGENT BUNDLE OF HIGHER ORDER . . 372
1. The Tangent Bundle of Order r and
Lifts of Functions 37 2
2. Lifts of Vector Fields 374
3. Lifts of 1 Forms and Tensor Fields . . 381
4. Local Expressions for Lifts of Tensor Fields 388
5. Lifts of Tensor Fields of Type (1, 1) . . 392
6. Lifts of Affine Connections . . . . 394
7. Lifts of Infinitesimal Transformations . . 399
8. The Tangent Group of Order r . . . . 401
9. Prolongations of G Structures to the
Tangent Bundle of Order r 404
10. Lifts of G Connections and Linear Holonomy
Groups in Tangent Bundles of Order r . . 409
Exercises 11 410
References 412
Index 421
|
| any_adam_object | 1 |
| author | Yano, Kentarō 1912-1993 Ishihara, Shigeru |
| author_GND | (DE-588)119350262 |
| author_facet | Yano, Kentarō 1912-1993 Ishihara, Shigeru |
| author_role | aut aut |
| author_sort | Yano, Kentarō 1912-1993 |
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| dewey-full | 516/.362 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.362 |
| dewey-search | 516/.362 |
| dewey-sort | 3516 3362 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV005716843 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:33:34Z |
| institution | BVB |
| isbn | 0824760719 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003571006 |
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| physical | IX, 423 S. |
| publishDate | 1973 |
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| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Yano, Kentarō 1912-1993 Verfasser (DE-588)119350262 aut Tangent and cotangent bundles differential geometry Kentaro Yano ; Shigeru Ishihara New York Dekker 1973 IX, 423 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 16 Faisceaux tangentiels Géométrie différentielle Geometry, Differential Tangent bundles Tangentialbündel (DE-588)4236004-3 gnd rswk-swf Kotangentialbündel (DE-588)4403097-6 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Tangentialbündel (DE-588)4236004-3 s DE-604 Kotangentialbündel (DE-588)4403097-6 s Ishihara, Shigeru Verfasser aut Pure and applied mathematics 16 (DE-604)BV000001885 16 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003571006&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yano, Kentarō 1912-1993 Ishihara, Shigeru Tangent and cotangent bundles differential geometry Pure and applied mathematics Faisceaux tangentiels Géométrie différentielle Geometry, Differential Tangent bundles Tangentialbündel (DE-588)4236004-3 gnd Kotangentialbündel (DE-588)4403097-6 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4236004-3 (DE-588)4403097-6 (DE-588)4012248-7 |
| title | Tangent and cotangent bundles differential geometry |
| title_auth | Tangent and cotangent bundles differential geometry |
| title_exact_search | Tangent and cotangent bundles differential geometry |
| title_full | Tangent and cotangent bundles differential geometry Kentaro Yano ; Shigeru Ishihara |
| title_fullStr | Tangent and cotangent bundles differential geometry Kentaro Yano ; Shigeru Ishihara |
| title_full_unstemmed | Tangent and cotangent bundles differential geometry Kentaro Yano ; Shigeru Ishihara |
| title_short | Tangent and cotangent bundles |
| title_sort | tangent and cotangent bundles differential geometry |
| title_sub | differential geometry |
| topic | Faisceaux tangentiels Géométrie différentielle Geometry, Differential Tangent bundles Tangentialbündel (DE-588)4236004-3 gnd Kotangentialbündel (DE-588)4403097-6 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Faisceaux tangentiels Géométrie différentielle Geometry, Differential Tangent bundles Tangentialbündel Kotangentialbündel Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003571006&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
| work_keys_str_mv | AT yanokentaro tangentandcotangentbundlesdifferentialgeometry AT ishiharashigeru tangentandcotangentbundlesdifferentialgeometry |