Lectures on differential geometry / Shlomo Sternberg.

Por: Sternberg, ShlomoSeries Prentice-Hall mathematics seriesEditor: Englewood Cliffs, N.J. : Prentice-Hall, c1964Descripción: xi, 390 p. : il. ; 24 cmTema(s): Geometry, DifferentialOtra clasificación: 58-01 (53-01)
Contenidos:
I 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. Ths 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]
4. Darboux's theorem [137]
7. Hamiltonian structures [141]
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]
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]
References [385]
Index [387]
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Libros Libros Instituto de Matemática, CONICET-UNS
Libros ordenados por tema 58 St839 (Browse shelf) Available A-2511

GEOMETRÍA II


Bibliografía: p. 385-386.

I 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. Ths 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] --
4. Darboux's theorem [137] --
7. Hamiltonian structures [141] --
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] --
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] --
References [385] --
Index [387] --

MR, 33 #1797

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