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| Авторизация |
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| Lee J.M. — Introduction to Smooth Manifolds |
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| Предметный указатель |
Homotopy, operator 274
Homotopy, relative to a set 142
Hopf map 170
Hyperplane 71
Hypersurface 235
Hypersurface in a Riemannian manifold 260
Hypersurface, induced volume form 260
Hypersurface, orientability 237
Ideal, differential 370
Identity of a Lie group 30
Identity, component 167
Identity, matrix 409
Image 407
Image of a Lie group homomorphism 169
Image of an embedding 118
Image of constant rank map 127
Immersed submanifold 119
Immersed submanifold of a manifold with boundary 120
Immersion 94
Immersion and constant rank 111
Immersion between manifolds with boundary 120
Immersion is locally an embedding 120
Immersion, composition of 97
Immersion, theorem, Whitney 134
Immersion, theorem, Whitney, strong 137
Immersion, vs. embedding 96
Implicit function theorem 109
Improper integral 241
Increasing multi-index 207
Independent, linearly 404
Index, conventions 12
Index, conventions for covectors 67
Index, lower 12
Index, position 12
Index, upper 12
Induced cohomology map 273
Induced Lie algebra homomorphism 378 379
Induced metric 191
Induced orientation on a boundary 239
Infinite-dimensional vector space 405
Infinitely differentiable 425
Infinitesimal generator 311 313
Infinitesimal generator of a flow 313
Infinitesimal generator of a global flow 311
Infinitesimal generator, invariant under flow 312 313
Injective group 296
Injective immersion vs. embedding 96
Inner product 184 421
Inner product, Euclidean 421
Inner product, space 421
Integrable 434
Integrable distribution 358
Integrable distribution is involutive 358
Integrable over a bounded set 436
Integrable, completely 359
Integrable, completely vs. involutive 359
Integral curve 307
Integral curve and one-parameter subgroup 382
Integral curve is immersed 313
Integral line 78 79
Integral line of a vector field 91
Integral line, fundamental theorem 81
Integral lower 434
Integral manifold 357
Integral manifold, union of 366
Integral manifold, uniqueness 360
Integral of a covector field diffeomorphism invariance 78
Integral of a covector field in  78
Integral of a differential form computing 245
Integral of a differential form over a manifold 242
Integral of a differential form over a smooth chain 297
Integral of a differential form over a smooth simplex 297
Integral of a differential form, diffeomorphism invariance 241 245
Integral of a differential form, linearity 244
Integral of a differential form, orientation reversal 244
Integral of a differential form, positivity 244
Integral of a function on a rectangle 434
Integral of a function on a Riemannian manifold 260
Integral of a function over a bounded set 436
Integral of an n-form in  240
Integral on a manifold 243
Integral on a manifold with corners 253
Integral over a 0-manifold 244
Integral over a boundary 244
Integral over a submanifold 244
Integral, improper 241
Integral, upper 434
Integrating a system of ODEs 309
Integration by parts 267
Integration on Lie groups 375
Integration, domain of 436
Integration, domain of, in a manifold 245
Integration, iterated 438
Interior is a manifold 21
Interior of a manifold with boundary 19 128
Interior, disjoint from boundary 20
Interior, multiplication 235
Interior, multiplication is an antiderivation 235
Intersection, transverse 128
Intertwine 149
Invariant under a flow 343
Invariant under a flow vs. Lie derivative 343
Invariant, left- 373
Invariant, tensor field 343
Invariant, tensor field and Lie derivative 343
Invariant, vector field 312 335
Inverse function theorem 105
Inverse map, smoothness of 99
Inverse of a matrix 410
Inversion map 30
Invertible linear map 408
Invertible matrix 409
Involutive 358
Involutive distribution and differential forms 369
Involutive vs. completely integrable 359
Inward-pointing 238
Isometric 187
Isometry 187 422
Isomorphic Lie algebras 373
Isomorphic locally 398
Isomorphic vector bundles 60
Isomorphic vector spaces 408
Isomorphism 408
Isomorphism, basis 408
Isomorphism, bundle 60
Isomorphism, determined by a basis 11
Isomorphism, Lie 32
Isomorphism, Lie algebra 373
Isomorphism, Lie group 32
Isomorphism, vector bundle 60
Isotropic immersion 222
Isotropic submanifold 222
Isotropic subspace 220
Isotropy group 147
Iterated integration 438
Jacobi identity 330 372
Jacobi identity for Poisson bracket 353
Jacobian matrix 51 425
k-covector 204
k-covector, elementary 206
k-form 212
k-slice in 97
k-slice in a manifold 97
Kernel 407
Kernel of Lie homomorphism is a subgroup 150
Kervaire, Michel 27
Killing field 344
Killing field, Euclidean 344 352
Kink 104
Kronecker delta 66
| Kronecker delta for multi-indices 206
Lagrangian immersion 222
Lagrangian, submanifold 222
Lagrangian, submanifold and closed 1-form 223
Lagrangian, subspace 220
Laplace operator 267
Laplacian 267
Leaf of a foliation 365
Lebesgue measure 434
Left action 145
Left G-space 146
Left translation 32 373
Left-invariant differential form 375
Left-invariant frame 375
Left-invariant tensor 375
Left-invariant vector field 373
Left-invariant vector field is complete 381
Length of a curve segment 186
Length of a curve segment in 90
Length of a curve segment, isometry invariant 187
Length of a curve segment, parameter independence 186
Length of a tangent vector 186
Length of a vector 421
Level set 104
Level set of submersion 113
Level set, regular 114
Level set, regular, is a submanifold 114
Level set, regular, of a real-valued function 114
Level set, regular, theorem 114
Level set, theorem, constant rank 113
Lie, algebra 371
Lie, algebra and one-parameter subgroups 382
Lie, algebra of  388
Lie, algebra of a Lie group 373
Lie, algebra of a subgroup 379 387
Lie, algebra, abelian 372
Lie, algebra, homomorphism 372 396
Lie, algebra, homomorphism, induced 378 379
Lie, algebra, isomorphic 373
Lie, algebra, isomorphism 373
Lie, algebra, product 372
Lie, algebra, representation 398
Lie, bracket 329
Lie, bracket, antisymmetry 330
Lie, bracket, bilinearity 330
Lie, bracket, coordinate expression 329
Lie, bracket, equals Lie derivative 333
Lie, bracket, is smooth 329
Lie, bracket, Jacobi identity 330
Lie, bracket, naturality 331
Lie, bracket, tangent to submanifold 331
Lie, covering group 380
Lie, covering group has isomorphic Lie algebra 380
Lie, derivative and invariant tensor field 343
Lie, derivative equals Lie bracket 333
Lie, derivative of a tensor field 339
Lie, derivative of a vector field 328
Lie, derivative of differential form 341
Lie, group 30
Lie, group is orientable 375
Lie, group is parallelizable 375
Lie, group, countable 32
Lie, group, covering of 167
Lie, group, discrete 32
Lie, group, finite 32
Lie, group, homomorphism 32 396
Lie, group, homomorphism is equivariant 149
Lie, group, homomorphism, image of 169
Lie, group, homomorphism, with discrete kernel 167
Lie, group, identity component 167
Lie, group, integration on 375
Lie, group, isomorphism 32
Lie, group, product of 32
Lie, group, simply connected 397
Lie, homomorphism 32
Lie, isomorphism 32
Lie, Sophus 398
Lie, Sophus, fundamental theorem 398
Lie, subalgebra 372
Lie, subgroup 124
Lie, subgroup, associated with Lie subalgebra 394
Lie, subgroup, closed 124
Lie, subgroup, embedded 124
Line integral 78 79
Line integral of a vector field 91
Line integral, fundamental theorem 81
Line integral, parameter independence 81
Line with two origins 21
Linear approximation 41
Linear approximation and the differential 74
linear combination 404
Linear functional 65
Linear group, complex general 31
Linear group, complex special 150
Linear group, general 31
Linear group, special 115 125
Linear map 407
Linear over  90
Linear system of PDEs 362
Linearly dependent 404
Linearly independent 404
Lipschitz, constant 432
Lipschitz, continuous 432
Local coframe 71
Local coordinate map 4
Local coordinate representation for a point 18
Local coordinates 4
Local defining function 116
Local defining function, existence 115
Local defining map 116
Local diffeomorphism 26
Local exactness of closed forms 279
Local flow 313
Local frame 60
Local frame and local trivialization 64
Local frame for a manifold 62
Local frame, orthonormal 188
Local isometry 187
Local one-parameter group action 313
Local operator 216
Local parametrization 191
Local section 28 59
Local section of smooth covering 28
Local section, existence of 111
Local trivialization 59
Local trivialization and local frame 64
Locally, Euclidean 3
Locally, finite 36
Locally, finite, cover 36
Locally, Hamiltonian 347
Locally, isomorphic 398
Lorentz metric 2 195
Lower, integral 434
Lower, sum 433
Lowering an index 193
Manifold is metrizable 191
Manifold is paracompact 37
Manifold with boundary, boundary point 128
Manifold with boundary, interior point 128
Manifold with boundary, product of 269
Manifold with boundary, push-forward 53
Manifold with boundary, smooth atlas 20
Manifold with boundary, smooth structure 20
Manifold with boundary, submanifold of 120
Manifold with boundary, tangent space 53
Manifold with boundary, topological 19
Manifold with boundary, vector field on 62
Manifold with corners 252
Manifold with corners, product of 269
Manifold with corners, Stokes’s theorem 254
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