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Kolar I., Michor P.W., Slovak J. — Natural Operations in Differential Geometry
Kolar I., Michor P.W., Slovak J. — Natural Operations in Differential Geometry

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Название: Natural Operations in Differential Geometry

Авторы: Kolar I., Michor P.W., Slovak J.

Язык: en

Рубрика: Математика/Геометрия и топология/Дифференциальная геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 434

Добавлена в каталог: 25.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^r$ -map      173
$\mathfrak{g}$-module homomorphism      131
A-admissible      341
A-velocity      306
Absolute differential      164
Absolute differential along X      163 164
Absolute operator      351
Action of a category      147
Adjoint representation      38
Admissible category      171
Affine bundle      60
Affine bundle functor on $\mathcal{M}f_m$      142
Albert      48
Algebraic bracket      68
Algebraic description of Weil functors      305
Almost complex structure      75
Almost Whitney-extendible      184
Anholonomic      16
Associated bundle      90
Associated map      171 174
Associated map to the k-th order operator A      143
Associated maps of the bundle functor F      139
Atiyah      265 266 267 295
Atlas      4
Base      11 50
Base extending      173
Base functor $B : \mathcal{F}\mathcal{M} \to \mathcal{M}f$      15
Baston      281 293 294 295
Bernstein      292
Bianchi identity      78
Boe      294
Boerner      131 281
Boman      172
Borel subalgebra      285
Bott      265 266 267 295
Branson      293 295
Broecker      10
Bundle functor on $\mathcal{C}$      170
Bundle functor on Mfm      138
Bundle functor on the category $\mathcal{M}f$      146
C-connection      365
C-field      175 365
Cahen      210
Canonical flip mapping      55 319
Canonical form on $P^1 M$      155
Canonical lift      59
CAP      252 254 393 416
Carrell      133 216 218
Cartan subalgebra      285
Category over manifolds      169
Cech cohomology set      51
Center      44
centralizer      44
Chart      4
Chart description of Weil functors      301
Chern forms      269
Chrastina      181 210
Christoffel forms      79
Classical complex Lie groups      32
Classifying spaces      94
Closed form      66
Cocurvature      73
Cocycle condition      51 77
Cocycle of transition functions      51 77
Cohen      11
Cohomologous      51 87
Cohomology classes      51
Collingwood      294
Complete connection      81
Complete flow      19
Complete vector field      19
Completely reducible      131
conformal      271
Conformal weight      293
Conjugation      38
Connection      73 77
Connection form, Lie algebra valued      100
Connection morphism      364
Connection, general      77 158
Connector      110 326
Contact (n, r)-element      124
Cotangent bundle      61
Covariant derivative      110 326
Covariant exterior derivative      103 111
Covelocities      120
Curvature      73 111
Curvature form, Lie algebra-valued      100
De Leon      356
De Wilde      210 252
Dekret      257
Derivation      6 322
Derivation, graded      67
Derived group      130
Descending central sequence      130
Dieudonne      9 17 133 216 218
Diffeomorphic      5
Diffeomorphism      5
Differential      8
Differential form      62
Differential group      119
Distinguished chart      27
distribution      24
Divergence      131
Donaldson      5
Doupovec      229 359 375
Dual natural vector bundles      142
Dual numbers      318
E-valued k-form      67 403
Eastwood      281 293 294
Eck      297 328 400 416
Effective action      44
Ehresmann      117 166 167 169 265
Ehresmann connection      81
Eilenberg      169
Elementary invariant      265
Elementary invariant tensors of degree r      214
Embedding      9
Epstein      116 168 188 210 295
Euler morphism      387
Evolution operator      29
Exact form      66
expansion      321
Expansion property      321
Exponential mapping      36
Exterior derivative      65
Exterior form      62
f -related      19 73
f-dependent      73
f-metric      278
Fegan      294
Feigin      292
Feng Luo      5
Fiber      50
Fiber bundle      76
Fiber bundle atlas      77
Fiber chart      77
Fiber over $x \in N$      15
Fiber r-jet at x      395
Fibered manifold      11
Fibered product      15
Finite order r      139
First polarization      219
Flow line      17
Flow of a vector field      18
Flow prolongation      59
Flow-natural transformation      336 338
Foliation      25
Formal curvature map      234
Formally real algebra      297
Frame bundle      122
Frame field      16 52
Frame form      95 154 156
Free action      44
Freedman      4 5
Froelicher      59 75 79 396
Froelicher — Nijenhuis bracket      69
Fuks      292
Fundamental vector field      46
G-atlas      86
G-bundle      86
G-bundle structure      86
G-equivariant      47
G-module      131
Gancarzewicz      345 357 416
Gauge natural bundle      395
Gauge natural operator      398
Gauge transformations      95
General connection      77 158
General linear group      30
General Ricci identity      235
Generalized Chern — Weil forms      403
Generalized covariant derivative      378
Generalized covariant differential      378
Generalized invariant tensor      230
Generalized invariant tensor theorem      230
Generalized Lie derivative      376
Germ of f at x      6
Gheorghiev      167
Gilkey      275 295
Global flow      19
Goldschmidt      340
Gompf      5
Grading      128
Graham      295
Grassmann manifold      88
Greub      5 81 115
Grozman      291
Gurevich      215
Gutt      210
Halperin      5 81 115
Higher order connections      160
Highest weight vector      285
Hilgert      48
Hirsch      10 11 82 180 314 330
Hochschild      201
Holonomic frame ?eld      16
Holonomous      61
Holonomy group      82 106
Holonomy Lie algebra      82
Homogeneous degree      131
Homogeneous function theorem      213
Homogeneous in the order      284
Homogeneous space      45
Homomorphism of G-bundles      92
Homomorphism over $\Phi$ of principal bundles      89
Horizontal bundle      78
Horizontal differential forms      103
Horizontal foliation      79
Horizontal lift      78 278
Horizontal projection      78
Horizontal space      73
Horizontal vector      78
I-equivalent      306
Ideal      43
Idealisator of a module      298
Idealizer      44
Immersed submanifold      12
Immersion      11
Induced action      172
Induced connection      107 108
Infinite jet      125
Infinite jet prolongation $J^{\infty} Y$ of Y      126
Infinitesimal automorphism      26
Infinitesimally admissible      170
Infinitesimally regular      365
Initial submanifold      12
Inner automorphism      38
insertion operator      63
Integrable distribution      25
Integral curve      17
Integral manifold      24
Invariant subspace      131
Invariant tensor of degree r      214
Invariant tensor theorem      214
Involution      55
Involutive distribution      28
Irreducible principle connection      107
Irreducible representation      131
Jacobson      42
Jaenich      10
Janyska      166 248 357 393
jet      117
Jet group      119
Jet of order $\infty$      125
Jet prolongation      117
Joris      12
k-admissible domain      176
k-form      62
Kainz      297 328
Kirillov      281 282 289 292 393
Kobak      363
Kobayashi      100 107 162 166 167 403
Kock      349
Kowalski      277 295
Kriegl      59 79 310
Krupka      248 252 357 360
Kurek      232 265 402
Lagrangian      387
Laptev      167
Leaf      25
Lecomte      48 252 404
Left action      44
Left invariant      33
Left logarithmic derivative      39
Leites      292
Libermann      115 167
Lichnerowicz      235 243
Lie algebra      17
Lie bracket of vector fields      17 325
Lie derivative      20 57 63 69
Lie group      30
Lie subgroup      41
Linear connection      109 110
Linear frame bundle      94
Linear vector field      379
Liouville vector field      257
Local category      169
Local diffeomorphism      5
Local isomorphism      170
Local operator      143
Local order      205
Local skeleton      170
Local trivialization      77
Local vector field      16
Localization of A over U      169
Locally flat category      185
Locally homogeneous      170
Locally non-constant      179
Lubczonok      248
Luciano      297 328
Luna      224
Malgrange      178
Mangiarotti      75 340
Mauhart      48 60
Maurer — Cartan form      39 79
Maximal integral manifold      24
Method of differential equations      245
Mikolasova      252
Mikulski      210 211 343 349 360
Milnor      4 301
1 2
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