Foundations of differential geometry: 2
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: | XV, 468 S. |
| ISBN: | 0471157325 9780471157328 |
Staff View
MARC
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| 100 | 1 | |a Kobayashi, Shōshichi |d 1932-2012 |e Verfasser |0 (DE-588)107956209 |4 aut | |
| 245 | 1 | 0 | |a Foundations of differential geometry |n 2 |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 XV, 468 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Interscience tracts in pure and applied mathematics |v ... | |
| 700 | 1 | |a Nomizu, Katsumi |d 1924-2008 |e Verfasser |0 (DE-588)119350238 |4 aut | |
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Record in the Search Index
| _version_ | 1804126065403101184 |
|---|---|
| adam_text | CONTENTS
OF
VOLUME
II
Chapter
VII
Submanifolds
1.
Frame bundles of a submanifold
..... 1
2.
The Gauss map
........ 6
3.
Covariant differentiation and second fundamental form
. 10
4.
Equations of Gauss and
Codazzi
..... 22
5.
Hypersurfaces in a Euclidean space
.... 29
6.
Type number and rigidity
...... 42
7.
Fundamental theorem for hypersurfaces
.... 47
8.
Auto-parallel submanifolds and totally geodesic submani¬
folds
.......... 53
Chapter
VIII
Variations of the Length Integral
1.
Jacobi fields
........ 63
2.
Jacobi fields in a Riemannian manifold
.... 68
3.
Conjugate points
. . . . . . .71
4.
Comparison theorem
....... 76
5.
The first and second variations of the length integral
. 79
6.
Index theorem of Morse
...... 88
7.
Cut loci
.........96
8.
Spaces of non-positive curvature
. . . . .102
9.
Center of gravity and fixed points of isometries
. .108
Chapter IX
Complex Manifolds
1.
Algebraic preliminaries
. . . . . .114
2.
Almost complex manifolds and complex manifolds
. . 121
3.
Connections in almost complex manifolds
. . .141
4.
Hermitian metrics and Kaehler metrics
. . . .146
5.
Kaehler metrics in local coordinate systems
. . .155
6.
Examples of Kaehler manifolds
. . . . .159
7.
Holomorphic sectional curvature
. . . . .165
8.
De
Rham decomposition of Kaehler manifolds
. . 171
XU CONTENTS
OF
VOLUME
II
9.
Curvature of Kaehler submanifolds
. . · .175
10. Hermitian
connections
in Hermitian
vector bundles. .
178
Chapter X
Homogeneous Spaces
1.
Invariant
affine
connections
. . . · · .186
2.
Invariant connections on reductive homogeneous spaces
. 190
3.
Invariant indefinite Riemannian metrics
. . · 200
4.
Holonomy groups of invariant connections
. . · 204
5.
The
de Rham
decomposition and irreducibility
. .210
6.
Invariant almost complex structures
. . . .216
Chapter XI
Symmetric Spaces
1. Affine
locally symmetric spaces
.....
^
2.
Symmetric spaces
......·· 225
3.
The canonical connection on a symmetric space
. · 230
4.
Totally geodesic submanifolds
. . . . · 234
5.
Structure of symmetric Lie algebras
. 238
6.
Riemannian symmetric spaces
.....
24j
7.
Structure of orthogonal symmetric Lie algebras
. · 246
8.
Duality
......... 253
9.
Hermitian symmetric spaces
...... 259
10.
Examples
......... 264
11.
An outline of the classification theory
.... 289
Chapter
XII
Characteristic
Glasees
1.
Weil homomorphism
....... 293
2.
Invariant polynomials
....... 298
3.
Chem
classes
........ 305
4.
Pontrjagin classes
....... 312
5.
Euler
classes
.... ... 314
Appendices
8.
Integrable
real analytic almost complex structures
. .321
9.
Some definitions and fects on Lie algebras
. . .325
CONTENTS OF VOLUME II
Xlii
Notes
12.
Connections and holonomy groups (Supplement to Note
1) 331
13.
The automorphism group of a geometric structure (Supple¬
ment to Note
9)........ 332
14.
The Laplacian
........ 337
15.
Surfaces of constant curvature in R3
. . . 343
16.
Index of nullity
........ 347
17.
Type number and rigidity of imbedding
. . . 349
18.
Isometric imbeddings
....... 354
19.
Equivalence problems for Riemannian manifolds
. . 357
20.
Gauss-Bonnet theorem
....... 358
21.
Total curvature
........ 361
22.
Topology of Riemannian manifolds with positive curvature
364
23.
Topology of Kaehler manifolds with positive curvature
. 368
24.
Structure theorems on homogeneous complex manifolds
. 373
25.
Invariant connections on homogeneous spaces
. . .375
26.
Complex submanifolds
....... 378
27.
Minimal submanifolds
....... 379
28.
Contact structure and related structures
. . .381
Bibliography
........ 387
Summary of Basic Notations
...... 455
Index for Volumes I and II
. . . . . 459
Errata for Foundations of Differential Geometry, Volume I
. 469
Errata for Foundations of Differential Geometry, Volume II
. 470
|
| 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 |
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| bvnumber | BV011542320 |
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| id | DE-604.BV011542320 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:11:32Z |
| institution | BVB |
| isbn | 0471157325 9780471157328 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007770005 |
| oclc_num | 263623009 |
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| physical | XV, 468 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 2 Shoshichi Kobayashi and Katsumi Nomizu Wiley classics library ed. New York [u.a.] Wiley 1996 XV, 468 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 2 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007770005&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 2 Shoshichi Kobayashi and Katsumi Nomizu |
| title_fullStr | Foundations of differential geometry 2 Shoshichi Kobayashi and Katsumi Nomizu |
| title_full_unstemmed | Foundations of differential geometry 2 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=007770005&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000931222 |
| work_keys_str_mv | AT kobayashishoshichi foundationsofdifferentialgeometry2 AT nomizukatsumi foundationsofdifferentialgeometry2 |