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Lee J.M. — Introduction to Smooth Manifolds
Lee J.M. — Introduction to Smooth Manifolds



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Название: Introduction to Smooth Manifolds

Автор: Lee J.M.

Язык: en

Рубрика: Математика/Геометрия и топология/Дифференциальная геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 474

Добавлена в каталог: 19.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Manifold, $C^k$      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 $\mathbb{R}^n$      130 434
Measure zero in $\mathbb{R}^n$ 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 $C^{\infty}(M)$      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 $GL(n, \mathbb{R})$      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 $GL(n,\mathbb{R})$      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 $\mathbb{R}^n$      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 $\mathbb{S}^{n-1}$      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 $\mathbb{R}^n$      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
1 2 3 4 5 6 7
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