Lectures on differential geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Chelsea Publ.
1983
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 442 S. graph. Darst. |
| ISBN: | 0828403163 0821813854 |
Staff View
MARC
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| 245 | 1 | 0 | |a Lectures on differential geometry |c Shlomo Sternberg |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY |b Chelsea Publ. |c 1983 | |
| 300 | |a XI, 442 S. |b graph. Darst. | ||
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| 650 | 4 | |a Géométrie différentielle | |
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Record in the Search Index
| _version_ | 1804117707658887168 |
|---|---|
| adam_text | Contents
! Algebraic Preliminaries 1
1. Tensor products of vector spaces 2
2. The tensor algebra of a vector space 5
3. The contravariant and symmetric algebras 10
4. Exterior algebra 14
5. Exterior equations 24
II Differentiable Manifolds 31
1. Definitions 32
2. Differential maps 39
3. Sard s theorem 45
4. Partitions of unity, approximation theorems 55
5. The tangent space 69
6. The principal bundle 73
7. The tensor bundles 84
8. Vector fields and lie derivatives 89
III Integral Calculus on Manifolds 97
1. The operator d 99
2. Chains and integration 104
3. Integration of densities 111
4. 0 and n dimensional cohomology, degree 120
5. Frobenius theorem 130
6. Darboux s theorem 137
7. Hamiltonian structures 141
IV The Calculus of Variations 148
1. Legendre transformations 150
2. Necessary conditions 153
3. Conservation laws 170
4. Sufficient conditions 174
5. Conjugate and focal points, Jacobi s condition 182
6. The Riemannian case 199
7. Completeness 207
8. Isometries 212
V Lie Groups 214
1. Definitions 214
2. The invariant forms and the Lie algebra 217
3. Normal coordinates, exponential map 222
4. Closed subgroups 228
5. Invariant metrics 231
6. Forms with values in a vector space 234
VI Differential Geometry of Euclidean Space 237
1. The equations of structure of Euclidean space 237
2. The equations of structure of a submanifold 244
3. The equations of structure of a Riemann manifold 246
4. Curves in Euclidean space 252
5. The second fundamental form 264
6. Surfaces 279
VII The Geometry of G Structures 293
1. Principal and associated bundles, connections 294
2. G structures 309
3. Prolongations 331
4. Structures of finite type 339
5. Connections on G structures 351
6. The spray of a linear connection 361
appendix i Two Existence Theorems 369
appendix ii Outline of Theory of Integration on E 374
APPENDIX ill An Algebraic Model of Transitive Differential Geometry 384
appendix IV The Integrability Problem for Geometrical Structures 417
References 435
Index 437
|
| any_adam_object | 1 |
| author | Sternberg, Shlomo 1936- |
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| bvnumber | BV003357752 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA641 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 370 |
| classification_tum | MAT 530f |
| ctrlnum | (OCoLC)9370359 (DE-599)BVBBV003357752 |
| dewey-full | 516.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/6 |
| dewey-search | 516.3/6 |
| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| isbn | 0828403163 0821813854 |
| language | English |
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| physical | XI, 442 S. graph. Darst. |
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| publisher | Chelsea Publ. |
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| spelling | Sternberg, Shlomo 1936- Verfasser (DE-588)121101762 aut Lectures on differential geometry Shlomo Sternberg 2. ed. New York, NY Chelsea Publ. 1983 XI, 442 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Géométrie différentielle Géométrie différentielle ram calcul variation inriac espace euclidien inriac groupe Lie inriac géométrie différentielle inriac théorème approximation inriac Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Differentialgeometrie (DE-588)4012248-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002120560&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sternberg, Shlomo 1936- Lectures on differential geometry Géométrie différentielle Géométrie différentielle ram calcul variation inriac espace euclidien inriac groupe Lie inriac géométrie différentielle inriac théorème approximation inriac Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4123623-3 |
| title | Lectures on differential geometry |
| title_auth | Lectures on differential geometry |
| title_exact_search | Lectures on differential geometry |
| title_full | Lectures on differential geometry Shlomo Sternberg |
| title_fullStr | Lectures on differential geometry Shlomo Sternberg |
| title_full_unstemmed | Lectures on differential geometry Shlomo Sternberg |
| title_short | Lectures on differential geometry |
| title_sort | lectures on differential geometry |
| topic | Géométrie différentielle Géométrie différentielle ram calcul variation inriac espace euclidien inriac groupe Lie inriac géométrie différentielle inriac théorème approximation inriac Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Géométrie différentielle calcul variation espace euclidien groupe Lie géométrie différentielle théorème approximation Geometry, Differential Differentialgeometrie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002120560&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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