Differential geometry of frame bundles:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer
1989
|
| Series: | Mathematics and its applications
47 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 234 S. |
| ISBN: | 0792300122 |
Staff View
MARC
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| 100 | 1 | |a Cordero, Luis A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Differential geometry of frame bundles |c Luis A. Cordero ; C. T. J. Dodson and Manuel de León |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer |c 1989 | |
| 300 | |a X, 234 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Mathematics and its applications |v 47 | |
| 650 | 7 | |a Connexion |2 Jussieu | |
| 650 | 7 | |a Faisceaux tangentiels |2 ram | |
| 650 | 7 | |a Fibré |2 Jussieu | |
| 650 | 7 | |a G-structure |2 Jussieu | |
| 650 | 7 | |a Géométrie différentielle |2 Jussieu | |
| 650 | 7 | |a Géométrie différentielle |2 ram | |
| 650 | 4 | |a Jets (Topologie) | |
| 650 | 7 | |a Prolongement |2 Jussieu | |
| 650 | 4 | |a Variétés différentiables | |
| 650 | 7 | |a Variétés différentiables |2 ram | |
| 650 | 4 | |a Differentiable manifolds | |
| 650 | 4 | |a Frame bundles | |
| 650 | 4 | |a Jets (Topology) | |
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| 700 | 1 | |a Leon, Manuel de |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1804116751385886720 |
|---|---|
| adam_text | Contents
Preface 1
1 The Functor J^ 3
Introduction 3
1.1 The Bundle J M —v M 3
Functorial properties of J* 5
Canonical lifts of vector fields to J*M 6
Two particular cases 7
Diffeomorphisms av^ and a)$ 8
1.2 J*G for a Lie group G 9
JlpG acting on J M 10
1.3 JpV for a vector space V 12
JpS for a Lie algebra g 12
1.4 The embedding jp 13
V = Rn 14
2 Prolongation of G structures 17
Introduction 17
2.1 Imbedding of J FM into FFM 17
2.2 Prolongation of G structures to FM 21
2.3 Integrability 25
2.4 Applications 29
Linear endomorphisms 30
Bilinear forms 33
Linear groups 36
3 Vector—valued differential forms 39
Introduction 39
3.1 General Theory 39
Particular cases 41
V = ®]Rn 42
V = ®SR 42
viii Contents
3.2 Applications 44
Prolongation of functions and forms 44
Complete lift of functions and tensor fields 49
Prolongation of G structures 52
4 Prolongation of linear connections 57
Introduction 57
4.1 Forms with values in a Lie algebra 57
4.2 Prolongation of connections 59
Local expressions 61
Covariant differentiation operators 61
4.3 Complete lift of linear connections 63
Parallelism 66
4.4 Connections adapted to G structures 68
4.5 Geodesies of Vc 70
4.6 Complete lift of derivations 71
5 Diagonal lifts 75
Introduction 75
5.1 Diagonal lifts 75
5.2 Applications 77
G structures from (1, l) tensors 77
G structures from (0,2) tensors 78
General tensor fields 79
6 Horizontal lifts 83
Introduction 83
6.1 General theory 83
6.2 Applications 85
Tensor fields 86
Linear connections 92
Geodesies 97
Covariant derivative 100
Canonical flat connection on FM 102
Derivations 104
7 Lift GD of a Riemannian G to FM 107
Introduction 107
7.1 GD, G of type (0,2) 107
7.2 Levi Civita connection of GD 110
7.3 Curvature of GD 113
7.4 Bundle of orthonormal frames 122
Contents ix
7.5 Geodesies of GD 125
7.6 Applications 125
/ structures on FM 125
Almost Hermitian structure 128
Harmonic frame bundle maps 134
8 Constructing G—structures on FM 137
Introduction 137
8.1 w associated G structures on FM 137
8.2 Defined by (l,l) tensor fields 139
8.3 Application to polynomial structures on FM 144
Example 1: /(3, l) structure on FM 146
Example 2: /(3, l) structure on FM 147
Example 3: /(4,2) structure on FM 148
Example 4: /(4, 2) structure on FM 148
Example 5: A family of examples 148
8.4 G structures defined by (0,2) tensor fields 149
8.5 Applications to almost complex and Hermitian structures 156
8.6 Application to spacetime structure 165
9 Systems of connections 171
Introduction 171
9.1 Connections on a fibred manifold 171
Local expressions 172
Examples of linear connections 173
Notation for sections 173
9.2 Principal bundle connections 174
Summary for the principal bundle of frames 177
9.3 Systems of connections 178
Examples of systems of linear connections 179
9.4 Universal Connections 180
9.5 Applications 183
Universal holonomy 183
Weil s Theorem 184
Spacetime singularities 185
Parametric models in statistical theory 187
10 The Functor J; 191
Introduction 191
10.1 The Bundle J$M — M 191
Functorial properties of Jf, 192
10.2 The second order frame bundle 193
x Contents
10.3 Second order connections 196
10.4 Geodesies of second order 200
10.5 G structures on F2M 202
10.6 Vector fields on F2M 203
10.7 Diagonal lifts of tensor fields 205
Algebraic preliminaries 205
Diagonal lifts of 1 forms 206
Diagonal lifts of (1, l) tensor fields 207
Diagonal lifts of (0,2) tensor fields 209
F2M for an almost Hermitian manifold M 212
10.8 Natural prolongations of G structures 212
Imbedding of J2FM into FF2M 213
Applications 214
Linear endomorphisms 214
Bilinear forms 215
10.9 Diagonal prolongation of G structures 215
Applications 217
Linear endomorphisms 217
Bilinear forms 217
Bibliography 219
Index 227
|
| any_adam_object | 1 |
| author | Cordero, Luis A. Dodson, Christopher T. J. 1941- Leon, Manuel de |
| author_GND | (DE-588)12958472X |
| author_facet | Cordero, Luis A. Dodson, Christopher T. J. 1941- Leon, Manuel de |
| author_role | aut aut aut |
| author_sort | Cordero, Luis A. |
| author_variant | l a c la lac c t j d ctj ctjd m d l md mdl |
| building | Verbundindex |
| bvnumber | BV002291566 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612.63 |
| callnumber-search | QA612.63 |
| callnumber-sort | QA 3612.63 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 350 SK 370 |
| ctrlnum | (OCoLC)18558207 (DE-599)BVBBV002291566 |
| dewey-full | 514/.224 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.224 |
| dewey-search | 514/.224 |
| dewey-sort | 3514 3224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 0792300122 |
| language | English |
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| publishDate | 1989 |
| publishDateSearch | 1989 |
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| publisher | Kluwer |
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| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Cordero, Luis A. Verfasser aut Differential geometry of frame bundles Luis A. Cordero ; C. T. J. Dodson and Manuel de León Dordrecht u.a. Kluwer 1989 X, 234 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 47 Connexion Jussieu Faisceaux tangentiels ram Fibré Jussieu G-structure Jussieu Géométrie différentielle Jussieu Géométrie différentielle ram Jets (Topologie) Prolongement Jussieu Variétés différentiables Variétés différentiables ram Differentiable manifolds Frame bundles Jets (Topology) Bündel Mathematik (DE-588)4193459-3 gnd rswk-swf Faserbündel (DE-588)4135582-9 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf n-Bein gnd rswk-swf Faserbündel (DE-588)4135582-9 s Differentialgeometrie (DE-588)4012248-7 s DE-604 n-Bein f Bündel Mathematik (DE-588)4193459-3 s Dodson, Christopher T. J. 1941- Verfasser (DE-588)12958472X aut Leon, Manuel de Verfasser aut Mathematics and its applications 47 (DE-604)BV008163334 47 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001505893&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cordero, Luis A. Dodson, Christopher T. J. 1941- Leon, Manuel de Differential geometry of frame bundles Mathematics and its applications Connexion Jussieu Faisceaux tangentiels ram Fibré Jussieu G-structure Jussieu Géométrie différentielle Jussieu Géométrie différentielle ram Jets (Topologie) Prolongement Jussieu Variétés différentiables Variétés différentiables ram Differentiable manifolds Frame bundles Jets (Topology) Bündel Mathematik (DE-588)4193459-3 gnd Faserbündel (DE-588)4135582-9 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4193459-3 (DE-588)4135582-9 (DE-588)4012248-7 |
| title | Differential geometry of frame bundles |
| title_auth | Differential geometry of frame bundles |
| title_exact_search | Differential geometry of frame bundles |
| title_full | Differential geometry of frame bundles Luis A. Cordero ; C. T. J. Dodson and Manuel de León |
| title_fullStr | Differential geometry of frame bundles Luis A. Cordero ; C. T. J. Dodson and Manuel de León |
| title_full_unstemmed | Differential geometry of frame bundles Luis A. Cordero ; C. T. J. Dodson and Manuel de León |
| title_short | Differential geometry of frame bundles |
| title_sort | differential geometry of frame bundles |
| topic | Connexion Jussieu Faisceaux tangentiels ram Fibré Jussieu G-structure Jussieu Géométrie différentielle Jussieu Géométrie différentielle ram Jets (Topologie) Prolongement Jussieu Variétés différentiables Variétés différentiables ram Differentiable manifolds Frame bundles Jets (Topology) Bündel Mathematik (DE-588)4193459-3 gnd Faserbündel (DE-588)4135582-9 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Connexion Faisceaux tangentiels Fibré G-structure Géométrie différentielle Jets (Topologie) Prolongement Variétés différentiables Differentiable manifolds Frame bundles Jets (Topology) Bündel Mathematik Faserbündel Differentialgeometrie n-Bein |
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| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT corderoluisa differentialgeometryofframebundles AT dodsonchristophertj differentialgeometryofframebundles AT leonmanuelde differentialgeometryofframebundles |