Foundations of differential geometry: 1
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1996
|
| Edition: | Wiley classics library ed. |
| Series: | Interscience tracts in pure and applied mathematics
... |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 329 S. |
| ISBN: | 0471157333 9780471157335 |
Staff View
MARC
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| 245 | 1 | 0 | |a Foundations of differential geometry |n 1 |c Shoshichi Kobayashi and Katsumi Nomizu |
| 250 | |a Wiley classics library ed. | ||
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1996 | |
| 300 | |a XI, 329 S. | ||
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Record in the Search Index
| _version_ | 1804126065396809728 |
|---|---|
| adam_text | CONTENTS
Interdependencc
of the Chapters and the Sections
. . xi
Chapter I
Differentiable Manifolds
1.
Differentiable manifolds
.......... 1
2.
Tensor algebras
............ 17
3.
Tensor fields
............. 26
4.
Lie groups
.............. 38
5.
Fibre bundles
............. 50
Chapter II
Theory of Connections
1.
Connections in a principal fibre bundle
...... 63
2.
Existence and extension of connections
...... 67
3.
Parallelism
.............. 68
4.
Holonomy groups
............ 71
5.
Curvature form and structure equation
..... 75
6.
Mappings of connections
.......... 79
7.
Reduction theorem
........... 83
8.
Holonomy theorem
........... 89
9.
Flat connections
............ 92
10.
Local and infinitesimal holonomy groups
..... 94
11.
Invariant connections
.......... 103
Chapter III
Linear and
Affine
Connections
1.
Connections in a vector bundle
........ 113
2.
Linear connections
........... 118
3. Affine
connections
........... 125
4.
Developments
............ 130
5.
Curvature and torsion tensors
........ 132
6.
Geodesies
.............. 138
7.
Expressions in local coordinate systems
...... 140
vii
viii CONTENTS
8.
Normal coordinates
........... 146
9. Linear infinitesimal
holonomy groups
...... 151
Chapter IV
Riemannian
Connections
1. Riemannian
metrics...........
154
2. Riemannian
connections..........
158
3. Normal
coordinates and convex neighborhoods
. . . 162
4.
Completeness
............. 172
5.
Holonomy groups
............ 179
6.
The decomposition theorem of
de
Rham
..... 187
7. Affine
holonomy groups
.......... 193
Chapter V
Curvature and Space Forms
1.
Algebraic preliminaries
.......... 198
2.
Sectional curvature
........... 201
3.
Spaces of constant curvature
........ 204
4.
Flat
affine
and
Riemannian
connections
..... 209
Chapter VI
Transformations
1.
Affine
mappings and
affine
transformations
.... 225
2»
Infinitesimal
affine
transformations
...... 229
3.
Isometries and infinitesimal isometries
...... 236
4.
Holonomy and infinitesimal isometries
..... 244
5.
Ricci
tensor and infinitesimal isometries
..... 248
6.
Extension of local isomorphisms
........ 252
7.
Equivalence problem
........... 256
Appendices
1.
Ordinary linear differential equations
...... 267
2.
A connected, locally compact metric space is separable
269
3.
Partition of unity
............ 272
4.
On an arcwise connected subgroup of a Lie group
. . 275
5.
Irreducible subgroups of 0{n)
........ 277
6.
Green s theorem
............ 281
7.
Factorization lemma
........... 284
contents
ix
Notes
1.
Connections
and holonomy groups
....... 287
2.
Complete
affine
and Riemannian connections
.... 291
3.
Ricci
tensor and scalar curvature
....... 292
4.
Spaces of constant positive curvature
...... 294
5.
Flat Riemannian manifolds
......... 297
6.
Parallel displacement of curvature
....... 300
7.
Symmetric spaces
............ 300
8.
Linear connections with recurrent curvature
.... 304
9.
The automorphism group of a geometric structure
. . 306
10.
Groups of isometries and
affine
transformations with
maximum dimensions
.......... 308
11. Conformai
transformations of a Riemannian manifold
. 309
Summary of Basic Notations
......... 313
Bibliography
............. 315
Index
............... 325
Errata for Foundations of Differential Geometry, Volume I
. 330
Errata for Foundations of Differential Geometry, Volume
Π
.331
|
| any_adam_object | 1 |
| author | Kobayashi, Shōshichi 1932-2012 Nomizu, Katsumi 1924-2008 |
| author_GND | (DE-588)107956209 (DE-588)119350238 |
| author_facet | Kobayashi, Shōshichi 1932-2012 Nomizu, Katsumi 1924-2008 |
| author_role | aut aut |
| author_sort | Kobayashi, Shōshichi 1932-2012 |
| author_variant | s k sk k n kn |
| building | Verbundindex |
| bvnumber | BV011542302 |
| ctrlnum | (OCoLC)263623007 (DE-599)BVBBV011542302 |
| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Wiley classics library ed. |
| format | Book |
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| id | DE-604.BV011542302 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:11:32Z |
| institution | BVB |
| isbn | 0471157333 9780471157335 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007769992 |
| oclc_num | 263623007 |
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| physical | XI, 329 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Wiley |
| record_format | marc |
| series2 | Interscience tracts in pure and applied mathematics |
| spelling | Kobayashi, Shōshichi 1932-2012 Verfasser (DE-588)107956209 aut Foundations of differential geometry 1 Shoshichi Kobayashi and Katsumi Nomizu Wiley classics library ed. New York [u.a.] Wiley 1996 XI, 329 S. txt rdacontent n rdamedia nc rdacarrier Interscience tracts in pure and applied mathematics ... Nomizu, Katsumi 1924-2008 Verfasser (DE-588)119350238 aut (DE-604)BV000931222 1 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007769992&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kobayashi, Shōshichi 1932-2012 Nomizu, Katsumi 1924-2008 Foundations of differential geometry |
| title | Foundations of differential geometry |
| title_auth | Foundations of differential geometry |
| title_exact_search | Foundations of differential geometry |
| title_full | Foundations of differential geometry 1 Shoshichi Kobayashi and Katsumi Nomizu |
| title_fullStr | Foundations of differential geometry 1 Shoshichi Kobayashi and Katsumi Nomizu |
| title_full_unstemmed | Foundations of differential geometry 1 Shoshichi Kobayashi and Katsumi Nomizu |
| title_short | Foundations of differential geometry |
| title_sort | foundations of differential geometry |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007769992&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000931222 |
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