|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Lee J.M. — Introduction to Smooth Manifolds |
|
|
|
| Предметный указатель |
Manifold,  9
Manifold, boundary 20
Manifold, complex 9
Manifold, oriented 232
Manifold, real-analytic 9
Manifold, Riemannian 184
Manifold, smooth 1 9
Manifold, smooth is a manifold with boundary 20
Manifold, smooth with corners 252
Manifold, topological 1 3
Map vs. function 23
Map, smooth, between manifolds 24
Mapping vs. function 23
Matrices of fixed rank 116
Matrices of maximal rank 13
Matrix of a linear map 409
Matrix upper triangular 420
Matrix, exponential 383
Matrix, Lie algebra 372
Matrix, skew-symmetric 412
Matrix, symmetric 115 412
Maximal flow 314
Maximal rank, matrices of 13
Maximal smooth atlas 9
Mayer — Vietoris sequence 288
Mayer — Vietoris sequence, connecting homomorphism 289
Mayer — Vietoris theorem for de Rham cohomology 288
Mayer — Vietoris theorem for singular cohomology 295
Mayer — Vietoris theorem for singular homology 294
Measure zero 254
Measure zero in  130 434
Measure zero in and smooth maps 130 131
Measure zero in manifolds 131
Measure zero in manifolds and smooth maps 132
Measure zero, n-dimensional 435
Measure zero, submanifolds 132
Metric 184
Metric, associated to a norm 423
Metric, Euclidean 185
Metric, flat 187 198
Metric, induced 191
Metric, pseudo-Riemannian 195
Metric, Riemannian 184
Metric, Riemannian in graph coordinates 191
Metric, Riemannian, existence 194
Metric, round 191 197
Metric, round in stereographic coordinates 197
Metric, space 184
Metrizable 191
Milnor, John 27
Minor of a matrix 413
Mixed tensor 179
Mixed tensor field 180
Mobius, band 265
Mobius, bundle 169 265
Mobius, transformation 162
Module 404
Moise, Edwin 27
Morse theory 325
Moser, Ju?rgen 351
Multi-index 206
Multi-index, increasing 207
Multilinear 172 415
Multilinear map and tensor product 178
Multilinear over  197
Multiplication, map 30
Multiplication, scalar 403
Munkres, James 27
n-dimensional measure zero 435
n-sphere 5
n-torus 14
n-torus as a Lie group 32
Natural action of  148
Natural action of O(n) 148
Naturality of the Lie bracket 331
Negatively oriented 231
Negatively oriented, chart 232
Negatively oriented, frame 232
Neighborhood, coordinate 4
Nonautonomous system of ODEs 326
Nondegenerate 2-tensor 195 219
Nonorientable manifold 232
Nonorientable manifold, de Rham cohomology 281
Nonsingular matrix 409
Norm 423
Norm of a tangent vector 186
Norm, associated metric 423
Norm, equivalent 423
Norm, topology 423
Normal bundle 139 199
Normal bundle is a submanifold 139
Normal bundle is a vector bundle 144
Normal bundle, orthonormal frame 144
Normal outward-pointing 261
Normal space 139
Normal vector 199
Normal vector field 260
Normed linear space 423
North pole 21
Nullity 411
O(N) see “Orthogonal group”
Odd permutation 414
ODE see “Ordinary differential equation”
One-parameter group action 310
One-parameter group action, local 313
One-parameter subgroup 381
One-parameter subgroup and integral curve 382
One-parameter subgroup and Lie algebra 382
One-parameter subgroup of  383
One-parameter subgroup of Lie subgroup 384
One-parameter subgroup, generated by X 383
Open ball 423
Open cover, regular 36
Open rectangle 433
Open submanifold 12 13
Open submanifold is embedded 97
Open submanifold, orientable 234
Open submanifold, tangent space 47
Orbit 146
Orbit is an immersed submanifold 167
Orbit, relation 153
Orbit, space 152
Order of a partial derivative 425
Ordered basis 406
Ordinary differential equation 308 309
Ordinary differential equation, autonomous 326
Ordinary differential equation, continuity theorem 320
Ordinary differential equation, existence theorem 314 318
Ordinary differential equation, integrating 309
Ordinary differential equation, nonautonomous 326
Ordinary differential equation, smoothness theorem 314 320
Ordinary differential equation, uniqueness theorem 314 317
Orientability of hypersurfaces 237
Orientability of parallelizable manifolds 234
Orientable 232
Orientable Lie group 375
Orientable manifold, de Rham cohomology 279
Orientable open submanifold 234
Orientation 230
Orientation and alternating tensors 231
Orientation and nonvanishing n-form 233
Orientation of a manifold 232
Orientation of a manifold, 0-dimensional 232 233
Orientation of a vector space 231
Orientation of a vector space, 0-dimensional 231
Orientation, covering 265
Orientation, form 233
Orientation, induced on a boundary 239
Orientation, pointwise 232
Orientation, pointwise, continuous 232
| Orientation, standard, of 231
Orientation, Stokes 239
Orientation-preserving 234
Orientation-preserving, group action 265
Orientation-reversing 234
Oriented basis 231
Oriented chart 232
Oriented chart, negatively 232
Oriented chart, positively 232
Oriented consistently 230
Oriented form 233
Oriented frame 232
Oriented frame, negatively 232
Oriented frame, positively 232
Oriented manifold 232
Oriented n-covector 232
Oriented negatively 231
Oriented vector space 231
Orthogonal 186 421
Orthogonal complement 423
Orthogonal group 114 125
Orthogonal group is a Lie subgroup 125
Orthogonal group is an embedded submanifold 114
Orthogonal group, action on  148
Orthogonal group, components 165
Orthogonal group, Lie algebra of 380
Orthogonal group, natural action 148
Orthogonal group, special 125
Orthogonal group, special, is connected 165
Orthogonal matrix 114
Orthogonal projection 423
Orthonormal basis 422
Orthonormal frame 188
Orthonormal frame, adapted 192 262
Orthonormal frame, existence 188
Outward-pointing 238
Outward-pointing, unit normal 261
Outward-pointing, vector field on boundary 238
Overdetermined 362
Paracompact 36
Paracompact, manifolds are 37
Parallelizable 62 375
Parallelizable, implies orientable 234
Parallelizable, Lie group 375
Parallelizable, spheres 64
Parallelizable, torus 64
parameter independence 81
Parametrization 105
Parametrization, local 191
Partial derivative 425
Partial derivative, higher order 425
Partial derivative, order of 425
Partial derivative, second order 425
Partial differential equations and the Frobenius theorem 361
Partition of a rectangle 433
Partition of an interval 433
Partition of unity 37
Partition of unity, existence 37
Passing to quotient 112
Path homotopic 255
PDE (partial differential equation) 361
Period of a differential form 303
Periodic curve 325
Permutation 183 204 206
Permutation, even 414
Permutation, odd 414
Piecewise smooth curve segment 79
Plane field 356
Poincare lemma 278
Poincare lemma for compactly supported forms 282
Pointwise, convergence 439
Pointwise, orientation 232
Pointwise, orientation, continuous 232
Poisson bracket 348
Poisson bracket on 348
Poisson bracket, commute 348
Poisson bracket, Jacobi identity 353
Polar coordinate map 19
Pole, north 21
Pole, south 21
Positions of indices 12
Positively oriented 231
Positively oriented chart 232
Positively oriented form 233
Positively oriented frame 232
Positively oriented n-form 232
Potential 82
Potential, computing 88
Precompact 36
Product of Hausdorff spaces 3
Product of Lie groups 32
Product of Lie groups, Lie algebra of 375
Product of manifolds with boundary 269
Product of manifolds with corners 269
Product of second countable spaces 4
Product, inner 184 421
Product, Lie algebra 372
Product, manifold, embedding into 94
Product, manifold, projection is a submersion 94
Product, manifold, smooth map into 26
Product, manifold, smooth structure 14
Product, manifold, tangent space 64
Product, rule 43
Product, semidirect 169
Product, smooth manifold structure 14
Product, symmetric 183
Product, symmetric, associativity 197
Projection of a vector bundle 59
Projection of product manifold is a submersion 94
Projection of the tangent bundle 57
Projection onto a subspace 408
Projection, orthogonal 423
Projective space is a manifold 6
Projective space is Hausdorff 6
Projective space is second countable 6
Projective space, complex 169
Projective space, covering of 167
Projective space, orientability 268
Projective space, quotient map is smooth 25 26
Projective space, real 6 14
Projective space, smooth structure 14
Proper, action 147
Proper, action of a discrete group 157
Proper, inclusion map vs. embedding 126
Proper, map 96
Properly discontinuous 158
Pseudo-Riemannian metric 195
Pullback 75
Pullback of a 1-form 76
Pullback of a 1-form in coordinates 77
Pullback of a covector field 76
Pullback of a covector field in coordinates 77
Pullback of a tensor field 181
Pullback of a tensor field in coordinates 182
Pullback of exterior derivative 218
Pullback of form 213
Pullback of form in coordinates 213
Push-forward 46
Push-forward and the differential 75
Push-forward between manifolds with boundary 53
Push-forward in coordinates 50
Push-forward of a vector field 62
Push-forward of a vector field by a diffeomorphism 63
Push-forward of tangent vector to curve 55
Push-forward, smoothness of 58
QR decomposition 166
Quaternions 401
Quotient by discrete group action 159
Quotient by discrete subgroup 160
Quotient of a vector space 407
|
|
|
| Реклама |
|
|
|
|
|
О проекте