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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 |
Divergence and volume decreasing flows 345
Divergence and volume increasing flows 345
Divergence and volume preserving flows 345
Divergence on nonoriented manifold 266
Divergence, product rule 267
Divergence, Theorem 262
Domain of integration 436
Domain of integration in a manifold 245
Domain of integration in the boundary of a manifold with corners 254
Domain, coordinate 4
Domain, flow 313
Domain, regular 238
Domain, restricting 121
Donaldson, Simon 27
Dot product 12 172 421
Dual basis 66
Dual basis, standard, for  66
Dual coframe 71
Dual homomorphism 295
Dual map 67
Dual space 66
Dual space, second 67
dV (in integral notation) 434
Dynamical systems 333
e (identity of a Lie group) 30
E(n) (Euclidean group) 161
Eigenfunction of Laplace operator 267
Eigenvalue of Laplace operator 267
Einselement 30
Einstein summation convention 12
Element, function 56
Elementary column operations 417
Elementary k-covector 206
Elementary matrix 417
Elementary row operations 417
Embedded subgroup 124
Embedded submanifold 97
Embedded submanifold, closed 126
Embedded submanifold, Embedded open 97
Embedded submanifold, image of embedding 98 118
Embedded submanifold, local characterization 97
Embedded submanifold, of a manifold with boundary 120
Embedded uniqueness of smooth structure 98
Embedding 94
Embedding composition of 97
Embedding image is an embedded submanifold 118
Embedding smooth 94
Embedding theorem, Whitney 136
Embedding theorem, Whitney, strong 137
Embedding topological 94
Equation, variational 321
Equivalent norms 423
Equivariant map 149
Equivariant rank theorem 150
Escape lemma 316
Euclidean dot product 12
Euclidean group 161
Euclidean inner product 421
Euclidean locally 3
Euclidean metric 185
Euclidean space 11 406
Euclidean space as a Lie group 31
Euclidean space as a manifold 11
Euclidean space, Lie algebra of 374
Euclidean space, smooth structure 11
Euclidean space, standard coordinates 11
Euclidean space, uniqueness of smooth structure 27
Evaluation map 373
Even permutation 414
Evenly covered 28
Exact 1-form 82
Exact covector field 82
Exact covector field on the torus 91
Exact form 219
Exact functor 296
Exact sequence 285
Exact sequence of complexes 286
Exact vs. conservative 83 85–87
Existence of Riemannian metric 194
Expansion by minors 419
Exponential map 385
Exponential map and one-parameter subgroups 385\
Exponential map is a local diffeomorphism 385
Exponential map of  385
Exponential map of a Lie group 385
Exponential map, push-forward 385
Exponential map, smoothness 385
Exponential of a matrix 383
Extension Lemma 39
Extension of smooth function 39
Exterior derivative 214 215 217
Exterior derivative and Lie brackets 352
Exterior derivative and pullback 218
Exterior derivative is local 216
Exterior differentiation 217
Exterior product 209
F-related 63
Face map 292
Faithful representation 398
Fake  27
Fiber of a map 112
Fiber of a vector bundle 58
Field plane 356
Figure eight 95
Figure eight as immersed submanifold 119
Figure eight is not embedded 126
Finite group as a Lie group 32
Finite, locally 36
Finite-dimensional representation 33
Finite-dimensional vector space 405
First-order system of PDEs 362
Flag 164
Flag, manifold 164
Flat 193
Flat, chart 359
Flat, chart for a foliation 365
Flat, metric 187 198
Flat, metric on torus 199
Flow 313
Flow is orientation preserving 326
Flow, domain 313
Flow, fundamental theorem on 314
Flow, fundamental theorem on, proof 315
Flow, generated by a vector field 314
Flow, global 310
Flow, global, arises from vector field 311
Flow, local 313
Flow, maximal 314
Flow, volume decreasing 345
Flow, volume decreasing and divergence 345
Flow, volume increasing 345
Flow, volume increasing and divergence 345
Flow, volume preserving 345
Flow, volume preserving and divergence 345
Foliation 365
Foliation, determines involutive distribution 365
Foliation, examples 365
Foliation, leaves of 365
Form, bilinear 173
Form, closed 85
Form, closed vs. exact 85–87
Form, conservative 82
Form, conservative vs. exact 83
Form, differential 70 212
Form, differential and orientation 233
Form, exact 82
Form, exact vs. closed 85–87
Form, exact vs. conservative 83
Form, left-invariant 375
Form, Lie derivative 341
| Forward reparametrization 81
Frame, global and trivial bundle 64
Frame, global for a manifold 62
Frame, left-invariant 375
Frame, local 60
Frame, local and local trivialization 64
Frame, local for a manifold 62
Frame, negatively oriented 232
Frame, oriented 232
Frame, orthonormal 188
Frame, orthonormal, adapted 192 262
Frame, orthonormal, existence 188
Frame, orthonormal, positively oriented 232
Free group action 147
Free vector space 175
Free vector space, characteristic property 175
Freedman, Michael 27
Frobenius theorem 359
Frobenius theorem and partial differential equations 361
Frobenius theorem, global 366
Frobenius theorem, global, proof 367
Function, element, smooth 56
Function, real-valued 23
Function, smooth, coordinate representation 24
Function, smooth, extension of 39
Function, smooth, on a manifold 24
Function, vector-valued 23
Function, vs. map 23
Functional, linear 65
functor 67
Functor, exact 296
Fundamental correspondence between Lie groups and Lie algebras 398
Fundamental theorem for line integrals 81
Fundamental theorem of Sophus Lie 398
Fundamental theorem on flows 314
Fundamental theorem on flows, proof 315
G-space 146
G-space, homogeneous 161
G-space, left 146
G-space, right 146
Gauss’s theorem 262
General linear group 13 31
General linear group, complex 31
General linear group, complex, Lie algebra of 402
General linear group, components 165
General linear group, connected 168
General linear group, is a manifold 13
General linear group, Lie algebra of 376
General linear group, natural action 148
General linear group, one-parameter subgroups 383
General position 291
Generalized chart 19
Generator, infinitesimal of a flow 313
Generator, infinitesimal of a global flow 311
Geometric simplex 291
Geometric tangent space 42
Geometric tangent vector 42
Geometry, differential v
Geometry, Riemannian 187
Germ 56
GL(V ) 31
Global coframe 71
Global flow 310
Global flow, arises from vector field 311
Global frame and trivial bundle 64
Global frame for a manifold 62
Global Frobenius theorem 366
Global Frobenius theorem, proof 367
Global trivialization 59
Global trivialization and global frame 64
Globally Hamiltonian 347
Gradient 71 193
Gradient, orthogonal to level set 199
Graph of a smooth function 103
Graph, coordinates on spheres 13
Graph, coordinates, Riemannian metric in 191
Graph, is an embedded submanifold 103
Grassmann manifold 15 17 164
Grassmann manifold is compact 169
Grassmannian 15 17 164
Grassmannian is compact 169
Green’s identities 267
Green’s Theorem 251
Group action 145
Group action, free 147
Group action, local one-parameter 313
Group action, one-parameter 310
Group action, orientation-preserving 265
Group action, proper 147
Group action, properly discontinuous 158
Group action, smooth 146
Group action, transitive 147
Group, circle 31
Group, circle, subgroup of  124
Group, complex general linear 31
Group, de Rham 272
Group, discrete 32
Group, general linear 31
Group, injective 296
Group, laws 310
Group, laws of a flow 313
Group, Lie 30
Group, special linear 115
Group, symmetric 414
Group, topological 30
Haar integral 376
Haar volume form 376
Half space, upper 19
Hamiltonian on  346
Hamiltonian, globally 347
Hamiltonian, locally 347
Hamiltonian, tangent to level sets 347
Hamiltonian, vector field 346 347
Harmonic function 267
Hausdorff product 3
Hausdorff space 3
Hausdorff subspace 3
Hermitian 151
Higher-order partial derivative 425
Hodge star operator 268
Hom(V, W) (space of linear maps) 196
Homeomorphism smooth 99
Homeomorphism, smooth 99
Homogeneous G-space 161
Homogeneous manifold 161
Homogeneous space 161
Homogeneous space, characterization theorem 162
Homologous submanifolds 303
Homology of a complex 286
Homology, singular 292
Homology, singular, smooth 296
Homomorphism, covering 380
Homomorphism, dual 295
Homomorphism, induced Lie algebra 379
Homomorphism, Lie 32
Homomorphism, Lie algebra 372
Homomorphism, Lie algebra, induced 378
Homomorphism, Lie group 32
Homomorphism, Lie group, is equivariant 149
Homotopic 142
Homotopic, maps are smoothly homotopic 143
Homotopic, path 255
Homotopic, relative to a set 142
Homotopic, smoothly 143
Homotopy 142
Homotopy, cochain 274
Homotopy, equivalence 274
Homotopy, equivalent 274
Homotopy, invariance of de Rham cohomology 276
Homotopy, inverse 274
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