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Lee J.M. — Differential and Physical Geometry
Lee J.M. — Differential and Physical Geometry



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Название: Differential and Physical Geometry

Автор: Lee J.M.

Язык: en

Рубрика: Математика/Геометрия и топология/Дифференциальная геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Количество страниц: 703

Добавлена в каталог: 20.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^*$ algebra      531
Adapted chart      98
Adjoint      303
Adjoint representation      304
Admissible chart      82
Almost complex manifold      284
Almost symplectic      507
Alternating      203 580
Antiholomorphic      283
Associated right action      312
Atlas      82
Atlas, submanifold      98
Base space      644
Boundary, manifold with      100 220
Bump function      125
Bundle map, local      27 638
Canonical 1­form      515
Cartesian product      xv
Cauchy — Bochner integral      20 625
Causal character      381
Cell complex      454
Chain rule      18 623
Chart      82
Chirality operator      490
Clifford algebra      482
Clifford group      485
Coadjoint action      506
Coisotropic      526
Complemented subspace      14 618
Complete vector field      168 169
COMPLEX      271
Complex manifold      284
Continuously differentiable      85
Contraction      576
Contragradient      117
Contravariant      567
coordinates      83
Cotangentt bundle      116
Covariant derivative      339
Covariant type      567
Co­distribution      329
Co­frame      124
Co­symplectic structure      526
Critical value      235
CW complex      454
Darboux's theorem      510
De Rham cohomology      211
Decomposable      152 571
Derivation      109 124 306
Derivation law      125
Derivative      17 622
Diffeomorphism      18 85 622
Differentiable      84
Differentiable structure      82
Differential      109 122
Differential complex      271
Differential form, vector valued      212
Differential, Lie      260
Discrete group action      94
Effective action      316
Endomorphism algebra      578
Equivariance      309 311
Euler — Lagrange equation(s)      501
Exponential map      262
Exterior derivative      209
Exterior product      204 580
Fiber bundle      461
Fiber derivative      517
Field tensor, electromagnetic      689
Flow      166
Flow box      167
Flow, local      166
Flow, maximal      169
Foliation      330
Foliation chart      330
Form, 1­form      121
Frame field      124
Free module      148 564 570
functor      554
Fundamental vector field      311 497
G bundle      250 462
General linear group      14 618
Geodesic      391
Geodesically complete      393
Germ of function      108
Germ of section      160
Germs      161
Graded algebra      580
Grassmannian      285
Half rank      504
Hamiltonian      500
Hamiltonian action      522
Hamiltonian vector field      514
hessian      246
Hilbert space      15 618
Holomorphic      283
Holonomic      123
Homomorphism presheaf      158
Homotopy equivalence      453
Hopf bundle      251 463
Identification      119
Immersion      238
Implicit function theorem      23 632
Index of a critical point      246
Infinitesimal automorphism      335
Infinitesimal symmetry      498
Initial submanifold      242
Integrable distribution      325
Interior product      216
Involutive distribution      324
Isometry      378
Isotropy subgroup      316 678
jet      157
Jet extension      157
k-algebra      148 564
Kahler manifold      509
Killing field      498
Lagrangian subspace      504
Leaf      334
Levi Civita derivative      389
Levi decomposition      303
Lie algebra action      521
Lie derivative      195
Lie derivative, of vector field      170
Lie derivative, on functions      124
Liebniz rule      125
Light cone      381
Lightlike curve      381
Lightlike subspace      381
Line bundle      144
Local diffeomorphism      22 627
Local immersion      25 26 634 635
Locally convex      129
Locally Hamiltonian      514
Locally splitting surjection      25 635
Lorentz manifold,      75
Maxwell's equations      689
Model space      81
Module      145 561
Momentum map      522
Morphism      552
Moving frame      124
Multilinear      15 149 565 619
Musical isomophisms, symplectic      510
Musical isomorphism      371
Nice chart      220
Nonnull curve      381
Nonnull vector      381
Null­homotopic      454
One parameter subgroup      136
Orbit      315
Orientable      219 220
Orientation      219 373 583
Orthogonal group      133
Paracompact      74
Partial tangent map      119
Partition of unity      129
Pauli matrices      136
Phase space      515
Piecewise smooth      381
Plaque      330
Poisson bracket      525
Poisson structure      526
Presheaf      158
Principal bundle      465
Product group      131
Product manifold      79
Product rule      19 625
Projective plane      78
Projective space      79
Proper time      382
Pull back      165
Pull­back      165
Push­forward      165
Reflexive      150 566
Regular distribution tangent subbundle      323
Regular Lagrangian      517
Regular point      235
Regular submanifold      98
Regular value      235
Riemann sphere      285
Riemann surface      286
Riemannian manifold      375
Rigid body      519
R­algebra      578
Sard's theorem      236
Scalar product      367 368
Scalar product bundle      474
semi-Riemannian      375
Sheaf      158
Skeleton      454
Smoothly universal      241
Spacelike      380
Spacelike curve      381
Spacelike subspace      381
Spin group      485
Splitting injection      23 633
Splitting surjection      24 634
Spray      362
Stable family      334
Star operator      473
Stationary      496
Stereographic projection      78
Stokes' theorem      228 229
Strong topology      529
Strongly Hamiltonian      522
Structure group      251 462 646
Subgroup, immersed      135
Subgroup, Lie      132
Submanifold      98
Submanifold atlas      98
Submanifold property      98
Submersion      243
Submodule      147 562
Support      227
Symplectic action      521
Symplectic form      505
Symplectic group      504
Symplectic manifold      505
Symplectic subspace      504
Symplectic vector field      514
Symplectic vector space      503
Tangent bundle      107 114
Tangent bundle of a foliation      331
Tangent map      27 113 637
Tangent space      27 108 637
Tangent vector      27 106 637
Tensor      181 574
Tensor derivation      192
Tensor map      182 566
Tensor product      151 567 569 572
Tensor product of tensor maps      184
Timelike curve      381
Timelike subspace      381
Timelike vector      381
Transitive      316
Transitive action      316
Transversality      247
Universal      151 569
Universal mapping      183 575
Vector bundle      594 644 645
Vector bundle chart      589
Vector bundle chart, type II      595 647
Vector bundle morphism      647
Weak topology      529
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