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| Авторизация |
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| Поиск по указателям |
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| Lee J.M. — Introduction to Smooth Manifolds |
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| Предметный указатель |
Subrectangle 433
Subspace of a vector space 404
Subspace of Hausdorff space 3
Subspace of second countable space 4
Subspace, affine 407
Subspace, coordinate 413
Subspace, projection onto 408
Sum, connected 128
Sum, direct 407
Sum, lower 433
Sum, upper 433
Summation convention 12
Support of a function 34
Support of a section 59
Support, compact 34
Supported in a set 34
Surface integral 264
Surface integral, Stokes’s theorem for 264
Sym (symmetrization) 182 205
Symmetric group 183 204 206 414
Symmetric matrix 115 412
Symmetric product 183
Symmetric product, associativity 197
Symmetric product, field 184
Symmetric tensor 182
Symmetrization 182 205
Symplectic basis 221
Symplectic complement 220
Symplectic coordinates 349
Symplectic form 221 346
Symplectic form, standard 222
Symplectic geometry 222
Symplectic group 227
Symplectic immersion 222
Symplectic manifold 221 346
Symplectic manifold, orientable 268
Symplectic structure 221
Symplectic structure on cotangent bundle 222
Symplectic structure, canonical, on  223
Symplectic structure, standard 222
Symplectic submanifold 222
Symplectic subspace 220
Symplectic tensor 219
Symplectic tensor, canonical form 221
Symplectic vector field 347
Symplectic vector space 219
Symplectomorphism 222
Tangent bundle 57
Tangent bundle, trivial 62
Tangent cotangent isomorphism 192 197
Tangent cotangent isomorphism, not canonical 198
Tangent covector 68
Tangent distribution 356
Tangent distribution and smooth sections 356
Tangent distribution, determined by a foliation 365
Tangent distribution, examples 357
Tangent distribution, spanned by vector fields 357
Tangent space to a manifold 45
Tangent space to a manifold with boundary 53
Tangent space to a submanifold 101 102 116
Tangent space to a vector space 48
Tangent space to an open submanifold 47
Tangent space to product manifold 64
Tangent space, alternative definitions 55
Tangent space, geometric 42
Tangent subbundle 356
Tangent to a submanifold 122
Tangent vector in Euclidean space 42
Tangent vector on a manifold 45
Tangent vector to a curve 54
Tangent vector to composite curve 55
Tangent vector to curve, push-forward of 55
Tangent vector, geometric 42
Tangent vector, local nature 47
Tangent, bundle is a vector bundle 59
Tangent, bundle, projection 57
Tangent, bundle, smooth structure 57
Tangent, bundle, standard coordinates 58
Tautologous 1-form 222
Taylor’s Formula 45
Tensor, alternating 202
Tensor, alternating and orientation 231
Tensor, alternating, elementary 206
Tensor, bundle 179 180
Tensor, contravariant 179
Tensor, covariant 172
Tensor, field 18
Tensor, field, contravariant 180
Tensor, field, covariant 180
Tensor, field, invariant under a flow 343
Tensor, field, Lie derivative of 339
Tensor, field, mixed 180
Tensor, field, smooth 180
Tensor, field, symmetric 184
Tensor, field, transformation law 196
Tensor, left-invariant 375
Tensor, mixed 179
Tensor, product and multilinear maps 178
Tensor, product of tensors 173
Tensor, product of vector spaces 176
Tensor, product of vectors 176
Tensor, product, characteristic property 176
Tensor, product, uniqueness 196
Tensor, symmetric 182
Time-dependent vector field 326
Top-dimensional cohomology of nonorientable manifold 281
Top-dimensional cohomology of orientable manifold 279
Topological boundary 20
Topological covering map 28
Topological covering map vs. smooth 28
Topological embedding 94
Topological group 30
Topological invariance of de Rham cohomology 277
Topological manifold 1 3
Topological manifold with boundary 19
Topology, norm 423
Torus 14
Torus as a Lie group 32
Torus of revolution 191 266
Torus, dense curve on 95 126
Torus, dense curve on, as immersed submanifold 119
Torus, dense curve on, is not embedded 126
Torus, dense subgroup of 125
Torus, exact covector fields on 91
Torus, flat metric on 199
Torus, Lie algebra of 375
Torus, parallelizable 64
Torus, smooth structure on 14
Total derivative 428
Total space 59
Trace 168
Transformation of coordinate vectors 52 68
Transformation of covector components 68 69 77
Transformation of vector components 52 69
Transition, map 7
| Transition, matrix 230 410
Transitive group action 147
Translation, left 32
Translation, lemma 309
Translation, right 32
Transpose of a linear map 67
Transpose of a matrix 412
Transposition 414
Transverse, intersection 128
Transverse, submanifolds 128
Transverse, vector 237
Transverse, vector field 237
Triangular matrix, upper 420
Triangulation 303
Triangulation, smooth 303
Trivial bundle 59
Trivial bundle and global frame 64
Trivial bundle, tangent 62
Trivialization, global 59
Trivialization, local 59
Trivialization, local and local frame 64
Tubular neighborhood 140
Tubular neighborhood theorem 140
U(n) (unitary group) 150
Uniform convergence 439
Uniqueness of quotients 113
Uniqueness of smooth structure 26
Uniqueness of smooth structure on embedded submanifold 98
Unit, circle 14
Unit, element of a Lie group 30
Unit, sphere 5
Unit, vector 421
Unitary group 150
Unitary group is connected 165
Unitary group, diffeomorphic to  167
Unitary group, Lie algebra of 402
Unitary group, special 150
Unitary group, special, is connected 165
Unitary group, special, Lie algebra of 402
Unity, partition of 37
Unity, partition of, existence 37
Universal covering group 380
Upper, half space 19
Upper, integral 434
Upper, sum 433
Upper, triangular matrix 420
Vanishes along a submanifold 123
Vanishes at points of a submanifold 123
Variational equation 321
Vector 404
Vector, addition 403
Vector, bundle 58
Vector, bundle, isomorphic 60
Vector, bundle, isomorphism 60
Vector, bundle, projection is a submersion 95
Vector, bundle, restriction of 59
Vector, bundle, section of 59
Vector, components 50
Vector, components, transformation law 52 69
Vector, contravariant 69
Vector, coordinate 50
Vector, covariant 69
Vector, field 60
Vector, field along a submanifold 199 236
Vector, field on a manifold with boundary 62
Vector, field, canonical form 331
Vector, field, commuting 335—337
Vector, field, complete 316 317
Vector, field, component functions of 60
Vector, field, conservative 91
Vector, field, coordinate 61
Vector, field, directional derivative of 327
Vector, field, globally Hamiltonian 347
Vector, field, Hamiltonian 347
Vector, field, invariant under a flow 335
Vector, field, invariant under a map 312
Vector, field, invariant under its own flow 312 313
Vector, field, Lie algebra of 372
Vector, field, line integral of 91
Vector, field, locally Hamiltonian 347
Vector, field, push-forward 62 63
Vector, field, restriction 122
Vector, field, smooth 60
Vector, field, smoothness criteria 60
Vector, field, space of 62
Vector, field, symplectic 347
Vector, field, time-dependent 326
Vector, field, transverse 237
Vector, geometric tangent 42
Vector, space 403
Vector, space over an arbitrary field 404
Vector, space, finite-dimensional 405
Vector, space, infinite-dimensional 405
Vector, space, oriented 231
Vector, space, real 403
Vector, space, smooth structure on 11
Vector, space, tangent space to 48
Vector, tangent on a manifold 45
Vector, tangent to composite curve 55
Vector, tangent, local nature 47
Vector, transverse 237
Vector-valued function 23
Vertex of a simplex 291
Volume 1 437
Volume and determinant 225
Volume of a rectangle 433
Volume of a Riemannian manifold 260
Volume, decreasing flow 345
Volume, decreasing flow and divergence 345
Volume, element, Riemannian 258
Volume, form, Riemannian 258
Volume, form, Riemannian in coordinates 258
Volume, form, Riemannian on a boundary 262
Volume, form, Riemannian on a hypersurface 260
Volume, increasing flow 345
Volume, increasing flow and divergence 345
Volume, measurement 201
Volume, preserving flow 345
Volume, preserving flow and divergence 345
Wedge product 209
Wedge product, Alt convention 212
Wedge product, anticommutativity 210
Wedge product, associativity 210
Wedge product, bilinearity 210
Wedge product, determinant convention 212
Wedge product, uniqueness 211
Weinstein, Alan 351
Whitney, approximation theorem 138
Whitney, approximation theorem on manifolds 142
Whitney, embedding theorem 136
Whitney, embedding theorem, strong 137
Whitney, Hassler 137
Whitney, immersion theorem 134
Whitney, immersion theorem, strong 137
Zero section 59
Zigzag lemma 286
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