|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Lee J.M. — Introduction to Smooth Manifolds |
|
|
|
| Предметный указатель |
Quotient of Lie group by closed normal subgroup 167
Quotient, manifold theorem 153
Quotient, passing to 112
Quotient, uniqueness of 113
Raising an index 193
Range, restricting 121
Range, restricting, embedded case 122
Rank of a linear map 94 411
Rank of a matrix 412
Rank of a smooth map 94
Rank of a tensor 173
Rank of a vector bundle 58
Rank, column 413
Rank, constant 94
Rank, constant, level set theorem 113
Rank, matrices of maximal 13
Rank, row 413
Rank, theorem 107
Rank, theorem, equivariant 150
Rank, theorem, invariant version 109
Rank-nullity law 105
Real projective space 6 14
Real projective space is a manifold 6
Real projective space is Hausdorff 6
Real projective space is second countable 6
Real projective space, smooth structure 14
Real vector space 403
Real-analytic manifold 9
Real-analytic structure 9
Real-valued function 23
rectangle 433
Rectangle as a manifold with corners 252
Rectangle, closed 433
Rectangle, open 433
refinement 36
Refinement, regular 37
Regular domain 238
Regular level set 114
Regular level set is a submanifold 114
Regular level set of a real-valued function 114
Regular level set, theorem 114
Regular open cover 36
Regular point 113
Regular point for a vector field 331
Regular refinement 37
Regular submanifold 97
Regular value 114
related see “F-related”
Relative homotopy 142
Reparametrization 81 186
Reparametrization of piecewise smooth curve 186
Reparametrization, backward 81
Reparametrization, forward 81
Representation of a Lie algebra 398
Representation of a Lie group 33
Representation, defining of  33
Representation, defining of  33
Representation, faithful 398
Representation, finite-dimensional 33
Restricting the domain of a map 121
Restricting the range of a map 121
Restricting the range of a map into a leaf of a foliation 361
Restricting the range of a map, embedded case 122
Restriction of a covector field 123
Restriction of a vector bundle 59
Restriction of a vector field 122
Retraction 141
Rham, de see “de Rham”
Riemann, integrable 434
Riemann, integral 434
Riemannian distance 188
Riemannian geometry 187
Riemannian manifold 184
Riemannian manifold as metric space 189
Riemannian metric 184
Riemannian metric existence 194
Riemannian metric in graph coordinates 191
Riemannian submanifold 191
Riemannian volume element 258
Riemannian volume form 258
Riemannian volume form in coordinates 258
Right 230
Right action 146
Right action is free 160
Right action is proper 160
Right action is smooth 160
Right G-space 146
Right translation 32
Right-handed basis 230
Round metric 191 197
Round metric in stereographic coordinates 197
Row operations, elementary 417
Row rank 413
Sard, Arthur 132
Sard’s theorem 132
scalar 404
Scalar, multiplication 403
Second countable 3
Second countable, product 4
Second countable, subspace 4
Second-order partial derivative 425
Section of a map 28
Section of a vector bundle 59
Section, local 28
Section, local, existence of 111
Section, local, of a vector bundle 59
Section, local, of smooth covering 28
Section, smooth 59
Section, zero 59
Segment, curve 79
Segment, curve, piecewise smooth 79
Segment, curve, smooth 79
Semidirect product 169
Series of functions, convergence 439
sgn (sign of a permutation) 204
Sharp 193
Short exact sequence of complexes 286
Sign of a permutation 204
Signature of a bilinear form 195
Simplex, affine singular 292
Simplex, geometric 291
Simplex, singular 292
Simplex, singular, boundary of 292
Simplex, smooth 296
Simplex, standard 291
Simply connected Lie group 397
Simply connected manifold 279
Simply connected manifold, cohomology of 279
Singular boundary 292
Singular boundary operator 292
Singular chain 292
Singular chain, complex 293
Singular chain, group 292
Singular cohomology 295
Singular cycle 292
Singular homology 292
Singular homology, group 292
Singular homology, isomorphic to smooth, singular 296
Singular homology, smooth 296
Singular matrix 409
Singular point for a vector field 331
Singular simplex 292
Singular simplex, affine 292
Singular simplex, boundary of 292
Skew-symmetric matrix 412
Slice in  97
Slice in a manifold 97
Slice, chart 97
Slice, coordinates 97
Smooth 7
| Smooth atlas 8
Smooth atlas on a manifold with boundary 20
Smooth atlas, complete 9
Smooth atlas, maximal 9
Smooth chain 296
Smooth chain group 296
Smooth chart 7 10
Smooth chart on a manifold with corners 252
Smooth chart with corners 252
Smooth coordinate map 10
Smooth covector field 70
Smooth covering map 28
Smooth covering map is a local diffeomorphism 28
Smooth covering map is open 28
Smooth covering map vs. topological 28
Smooth covering map, injective 28
Smooth curve 54
Smooth dynamical systems 333
Smooth embedding 94
Smooth function element 56
Smooth function on a manifold 24
Smooth function, coordinate representation 24
Smooth function, extension of 39
Smooth group action 146
Smooth homeomorphism 99
Smooth manifold 1 9
Smooth manifold is a manifold with boundary 20
Smooth manifold, structure 9
Smooth map between Euclidean spaces 7 425
Smooth map between manifolds 24
Smooth map from a subset of 428
Smooth map from base of covering 29
Smooth map into a product manifold 26
Smooth map is a local property 24 25
Smooth map, composition of 25
Smooth map, coordinate representation 25
Smooth section 59
Smooth simplex 296
Smooth singular homology 296
Smooth singular homology, isomorphic to singular 296
Smooth structure 9
Smooth structure on 11
Smooth structure on a manifold with boundary 20
Smooth structure on a vector space 11
Smooth structure on spheres 27
Smooth structure on the tangent bundle 57
Smooth structure with corners 252
Smooth structure, uniqueness 26
Smooth structure, uniqueness, on  326
Smooth structure, uniqueness, on 27
Smooth triangulation 303
Smooth vector field 60
Smoothly compatible charts 7
Smoothly compatible charts with corners 252
Smoothly homotopic 143
Smoothness is local 24 25
Smoothness of inverse maps 99
SO(3) is diffeomorphic to P3 168
SO(n) (special orthogonal group) 125
South pole 21
Space, vector 403
Space, vector over an arbitrary field 404
Space, vector, real 403
span 404
Special linear group 115 125
Special linear group, complex 150
Special linear group, connected 168
Special linear group, Lie algebra of 388 402
Special orthogonal group 125
Special orthogonal group is connected 165
Special unitary group 150
Special unitary group is connected 165
Special unitary group, Lie algebra of 402
Sphere 5
Sphere is an embedded submanifold 103 114
Sphere is orientable 237 239 265
Sphere, de Rham cohomology 290
Sphere, different smooth structures on 27
Sphere, parallelizable 64
Sphere, standard smooth structure 13
Sphere, stereographic coordinates 21
Sphere, vector fields on 64
Spherical coordinates 104
Square, homeomorphic to circle 7
Square, not diffeomorphic to circle 127
Standard basis 406
Standard coordinates on 11
Standard coordinates on the tangent bundle 58
Standard dual basis for 66
Standard orientation of 231
Standard simplex 291
Standard smooth structure on 11
Standard smooth structure on  13
Standard smooth structure on a vector space 11
Standard symplectic form 222
Standard symplectic structure 222
Star operator, Hodge 268
Star-shaped 87 278
Starting point of an integral curve 308
Stereographic projection 21
Stereographiccoordinates 21
Stereographiccoordinates, round metric in 197
Stokes orientation 239
Stokes’s theorem 248
Stokes’s theorem for surface integrals 264
Stokes’s theorem on manifolds with corners 254
SU(2) is diffeomorphic to S3 167
SU(n) (special unitary group) 150
Subalgebra, Lie 372
Subbundle 356
Subbundle, tangent 356
Subcover, countable 4
Subgroup, closed is embedded 394
Subgroup, closed of a Lie group 392
Subgroup, dense, of the torus 125
Subgroup, discrete 160
Subgroup, discrete, quotient by 160
Subgroup, Lie 124
Subgroup, one-parameter 381
Subinterval 433
Submanifold 120
Submanifold, calibrated 304
Submanifold, closest point 144
Submanifold, embedded has measure zero 132
Submanifold, embedded of a manifold with boundary 120
Submanifold, embedded open is embedded 97
Submanifold, embedded, curve in 128
Submanifold, embedded, immersed 119
Submanifold, embedded, local characterization 97
Submanifold, embedded, open 97
Submanifold, embedded, open tangent space 47
Submanifold, embedded, restricting a map to 122
Submanifold, embedded, uniqueness of smooth structure 98
Submanifold, regular 97
Submanifold, restricting a map to 121
Submanifold, restricting a map to embedded case 122
Submanifold, Riemannian 191
Submanifold, tangent space 101 102
Submanifold, tangent space and defining maps 116
Submanifold, transverse 128
Submersion 94
Submersion and constant rank 131
Submersion into  127
Submersion is a quotient map 111
Submersion is open 111
Submersion, composition of 97
Submersion, level set of 113
Submersion, passing to quotient 112
Submersion, theorem 113
Subordinate to a cover 37
|
|
|
| Реклама |
|
|
|
|
|
О проекте