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Sternberg Sh. — Lectures on Differential Geometry
Sternberg Sh. — Lectures on Differential Geometry



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Название: Lectures on Differential Geometry

Автор: Sternberg Sh.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Количество страниц: 390

Добавлена в каталог: 19.11.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adjoint representation      227
Adjoint system      28
Algebra of contravariant tensors      10
Algebraic preliminaries      1
Almost continuous      113
Ambrose — Singer Theorem      305
Antiderivation      21 102
Antisymmetric tensors      14
Approximation theorems      55
ARC      207
Associated bundle      307
Associated system      24
Barycentric coordinates      104 105
Bases      8
Betti numbers      289
Bi-invariant Riemann metric      232
Bianchi — Cartan identities      330
Bianchj's identities      360
Bilinear map      2
binomial      253
Bonnet's theorem      292
Buler vector field      159
Bundle of frames      80
Bundle of orthonormai frames      247
Calculus of variations      148
Cartan's Lemma      18
Cellulated surface      288
Characteristic system      135
Classical mechanics      141
Closed differential form      108
Closed subgroups      228
Closed submanifold      43
Cohomology group      108
Complete Riemannian manifold      173
Complete spray      199
Completely integrable      130
Completeness      207
Conjugate points      182
Connection form      298
Connection on a principal bundle      298
Connection on an associated bundle      308
Connections      294
Conservation laws      170
Conservation of energy      146
Content      113
Content zero      113
Contraction of tensors      6
Contravariant and symmetric algebras      10
Contravariant degree      6
Contravariant vector field      79
Coordinate chart      35
Coordinate map      34
Coordinate neighborhood      34
Coordinates of die chart      36
Cotangent bundle      79
Covariant degree      6
Covariant derivative, with respect to a linear connection      352
Covariant derivative, with respect to a parallelism      341
Covariant differential      355
Covariant vector field      79
Critical points      47
Critical value      47
Cross section      295
Curvature of a connection      300
Curvature of a ribbon      253
Curves in Euclidean space      252
Darboux's theorem      137 141
Decomposable p-vectors      19
Degree of a map      120
densities      111 112
Derivation      102
Diffeomorphism      43
Differentiable function      45
Differentiable manifolds      31 35
Differentiable p-chains      106
Differential form of degree p      82
Differential system      130
Energy of a Lagrangian      152
Equations of structure of Euclidean space      237 238
Equations of structure, of a Riemann manifold      246 249
Equations of structure, of a submanifold      245
Equations of structure, of a submanifold of Euclidean space      251
Euler — PoincarЈ characteristic      290
Euler's differential equation      159 166
Exact differential form      108
Exponential map      222
Exterior 2-fornis      23
Exterior algebra      14. 15
Exterior differential form of degree p      82
Exterior differentiation      100
Exterior equations      23
Exterior forms      20
Exterior multiplication      20
Extremal      167
F-related      95
Field of quantities      78
Flat G-structure      315
Focal point      18
frames      8
Frenet equations      253
Frenet ribbon      253
Frenet trihedral      253
Frobenius' Theorem      130
Fundamental form      143
G-connection      352
G-structures      293 310
Gauss' lemma      201
Gaussian curvature      266
General equivalence problem      314
Geodesic flow on T(M)      199
Geodesic spray      200
Geodesies of a Riemann metric      167
Hamilton — Jacobi equation      179
Hamiltonian manifold      141
Hamiltonian structures      141
Hamiltonian vector field      143
Higher order structures      337
Holonomy group      300 301
Homogeneous ideal      26
Homomorphism of principal bundle      294
Horizontal vector field      299
Imbedding      42
Immersed submanifold      43
Immersion      42
Indefinite metric      13
Inner product      22
Integral calculus on manifolds      97
Integral manifold      130
Interior multiplication      20
Invariant metrics      231
Isometries      212
Isomorphism of principal bundles      294
Jacobi equations      186
Jacobi vector field      185
Jacobi's condition      182
Jacobi's identity      94 222
kinetic energy      149
Knbayashi's theorem      347
Left invariant forms      217
Left invariant spray      222
Left invariant vector fields      218
Legendre transformations      150
Lensor algebra of a vector space      5
Levi — Civita's theorem      334
Lie algebra      94 217 218
Lie bracket      94
Lie derivatives      89 91
Lie groups      214
Lie homomorphism      216
Lie subgroups      216
Linear connection      352
Linear differential form      79
Linear map      2
Linear quantity      10
Liouville form      171
Locally bounded      112
Lorentzian metric      14
Maurer — Cartan equation      218
Maximal integral manifold      136
Moving frames      244
Multilinear map      3
Necessary conditions for a minimum      153
Non-singular metric      13
Normal coordinates      222
One parameter group      89
Operator D      99
Orientable      115
Orientation on a manifold      116
Oriented manifold      116
Orthogonal frames      240
Partitions of unity      55 57
Path      207
Poincare's lemma      121
Poisson bracket      142
Positive definite Lagrangian      176
Principal bundles      73 294
Principal normal      253
Prolongations of $g\;\subset\;Hom(V, M)$      331
Prolongations of a G-structure      331
Proper imbedding      43
Proper map      43
quantities      73 76
Rank of a collection of functions      341
Ray      208
Regular family of functions      342
Regular Lagrangian      152
Restricted equivalence problem      339
ribbon      252
Right interior multiplication      22
Sard's theorem      45
Scalar densities      10
Scalar product      22
Second fundamental form      264
Second order differential equation      166
Second order structures      337
Segment      207
Singulars-simplex      106
Space of exterior p-forms over V      20
Space of m-frames of V      36
Space of symmetric tensors      12
Spherical map      264
Spray      199
Spray of a linear connection      361
Stokes' theorem      109 119
Structure function of a G-structure      318
Structure group of a bundle      294
Sturm's theorem      291
Submanifold      43
Sufficient conditions in the calculus of variations      174
Support of a density      112
Support of a form      109
Surfaces      279
Symmetric bilinear forms      13
Symmetric tensors      14
Tangent space      69 70
Tangent vector      69
Tensor bundles      84
Tensor field      80
Tensor products of vector spaces      2 4 5
Theorem Egregium      267
Thorn's transversality theorem      65
Topological group      231
Torsion of a curve      253
Torsion of a linear connection      356
Torsion of a ribbon      253
Total angular momenta      147
Total linear momenta      147
Transitive G-structures      321
Trivial bundle      295
Twist of a ribbon      253
Universal property      1C
Vector fields      89
Vector product      23
Vector space      2
Vector valued forms      234
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