Hermann R. — Differential geometry and the calculus of variations :: Электронная библиотека попечительского совета мехмата МГУ

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Hermann R. — Differential geometry and the calculus of variations

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Название: Differential geometry and the calculus of variations

Автор: Hermann R.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1968

Количество страниц: 443

Добавлена в каталог: 14.10.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Abelian      95
Abelian group      180
action      135 136
Addition formula      233 239
Adjoint action      88 90
Affine connection      261 262 269 270 313 378 381 384 425 427
Affine transformations      89
Algebra      73
Algebraic topology      62
Arc length      274
Arcwise connected      24
Associative law      81
Atlas      24
Augmented index      414
Automorphism      342
Autonomous system      36
Barriers      36
Betti number      182
Bianchi identities      341
Boundary      113
Boundary condition      402 406 415
Bounded operator      94
Bracket      87
Calculus of variations      99 130 151—153
Carlan — Maurcr form      217
Cartan form      118
Cartan subalgebra      228
Cartan subgroup      227
Cartan-one form      154 170 183 213
Cauchy — Ricnmnn equations      421
Celestial mechanics      136 137 139 231
Characteristic      154 167 175 182 184 189 213 363 364 394 400
Characteristic curve      118 147 171 172
Characteristic function      162
Chart      24
Chow’s theorem      247
Christoffel symbols      262 324
Classical groups      96
Classical mechanics      81 98 152 179 427
Closed subgroups      92
Commutator      84
Compact      6 24
Compatible mapping      309
Complete solution      137
Completely integrable      68
Completely integrable systems      71
Completely integrable vector field system      78
Completeness      285 287 293 299
Completion of a path system      243
Complex Lie algebra      84
Complex lie algebra, Manifold      420 426
Complex lie algebra, submanifold      422
Complex lie algebra, vector space      96
Configuration space      176 185 219 429
Conformal Riemannian metric      288
Conjugate point      293 294 296 299 305 313 316 332 411
Connected component      345
Connected Lie group      91
Connected subgroup      92
Connection      24 95 97
Connection automorphism      379 380 384
Connection forms      324 336 381
Cononical coordinate system      95
Cononical coordinate system of the second kind      95
Cononical form      40 125 178
Cononical neighborhood      95
Cononical transformations      81 141 179 231
Conservation laws      100
Conserved quality      99 429
Constant curvature      359
Constraint subset      117
Continuous induction      284
Continuous mechanics      104
Contraction      11 47 114
Convex      21 376
Convexhypersurface      375
Coordinate neighborhood      24 51
Coordinate patch      62
Coordinate system      25
cosets      93
Covariant      98
Covariant derivative      293 310 312 339 357 359 360 425
Covariant differentiation      262—264 268 269
Covariant tensors      25
Covector      11 12 17 19 20 23
Covering      24
Covering space or map      286 290
Critical points      114 147 181 242
Cross section      9 10 17—20 22 26 63
Curl      3 99
Curvature      266 297 303 323 326 335 359 382
Deformation      152 153
Deformation of submanifolds      362
Derivation      10 22 23 34 63
Determinant      14 17 20 64
Developable surface      362 365
Diffeomorphism      25 28 39 51
Differential      19 25
Differential forms      4 14 17—20 23 27 46
Differential ideal      113
Differential manifold      23 27
Differential one parameter subgroup      88
Differential operator      10 34 402
Dirac delta function      56
Disconnected      97
Distance function      281 282
Divergence      3 139 386 399
Domain      21 23 35 39 107
Domain of convergence      83
Domain of holomorphy      426
Dot product      3
Dual mapping      15
Dual space      11
Duality principle for path system      250
Dynamics      102
d’Alembertian      386
d’Alembert’s principle      102 109 151 427 428
Earth      140
Eigenvalue      209 210 337 390
Einsteinian mechanics      188 192
Electromagnetism      98
Elliptic functions      227 232 240
Elliptic integral      235
Elliptical orbit      140
Energy      99 207
entropy      254
Equation of continuity      106
Euclidean dot product      98
Euclidean geometry      102 106
Euclidean space      3 22 24 98 164 276
Euler angles      223 224 227 231
Euler equations      42 99 103 151—154 163 168 169 222 299
Euler relation      161 165 184 389
Eulerian      104
Euler’s equations of fluid motion      108
Exponential mapping      91
Extended curve      154
Exterior algebra      113 177 178
Exterior derivative      20 46 113
Exterior differentiation      18
Exterior product      12
External forces      100
Extremal      116 152 158 165 171 174 183 184
Extremal curve      119
Extremal field      142 143 162—164 168 173
Fermat’s principle      168
Fiber      9
Fiber bundle      348 349
First fundamental form      319
Flat coordinate system      66

Fluid mechanics      98
Focal point      330 331 344 403 407 408
Foliation      71
Force law      98
Foundations of Lie group theory      90 437
Frobenius complete integrability      364
Functional analysis      85
Functionally independent      75 79
Fundamental solution      393
Galilean group      192 199 203 207—209
Galilean transformation      194
Gaussian curvature      308 362 366
General position      31 33
General relativity      399
Generalized functions      56 59
Generalized manifold      349
Geodesic deformation      292
Geodesic hall      288
Geodesic triangle      308
Geodesically convex      334 335
Geodesics      191 261 275 278 282 285 286 292 297 299 314 331
Geometric physical compatibility conditions      374 400
Geometrical optics      136
Global integrals      71
Gradient      3 277 336 386
Gram — Schmidt orthogonalization      320
Grassman manifolds      93
Grassman variety      359
Gravitation      98
Greens, formula      393
Group      81
Hamilton equations      99 103 104 118 129 130 132 134 136 140 154 155
Hamilton — Jacobi equation      134 135 137 139 173 386 389
Hamilton — Jacobi partial differential equation      131
Hamilton — Jacobi theory      122 129 130 134 136 139 168 174
Hamiltonian      130—132 137—141 154 155 178 182 185 186 215 225 226
Hamiltonian system      179
Harmonic function      390 393
Hausdorff      6 24
Hermatian bilinear      96
hessian      147 375 377
Hilbert space      94
Holomorpic      420
Homeomorphism      71 87 91 177
Hopf — Rinow theorem      284 286 289 301
Hyperplanoids      424
Hypersurface      59 60 107 336
Ideal      175
identity map      92
Immersed submanifold      318
Immersion      30 32
Implicit function theorem      25 28 33 58
INDEX      404
Infinite dimensional      82
Infinite dimensional manifold      114 241
Infinitesimal deformation      114 116 121 152 280 293
Infinitesimal generator      44 83 87—89 95 159 354 378
Infinitesimal version of adjoint action      90
Inner product      12
Integrability condition      65 421
integral      40 51
Integral curve      35 44 68 89
Integral curves, of vector fields      178
Integral equation      85
Integral function      64 75
Integral geometry      50 57 59
Integral manifold      116
Integral map      64
Integral submanifold      67 123 124 126 127
Integration factor      252
Integration on manifolds      60
Integration over fibers      55 57
Intersection      31
Inverse      81
Inverse function theorem      28
Involution      179
Involutive automorphism      228
Isoenergetic reduction      190
Isometric      287 362
Isometric imbedding      362 366 368
Isometries      342 361
Isomorphic      78
Isoparametric function      391
Isotropy subgroup      93 94 343 346 353 359
Jacobi identity      35 84
Jacobi vector fields      291 293 294 297 298 315 331 333 356
Jacobi-bracket      18 34 36 37 44 63 263 353
Jacobian      51 135 138
Jacobian matrix      25
Kepler problem      141
Kernel      16
Killing form      430
Killing vector field      354—356 359
kinetic energy      99 100 102 156 186
Kronecker delta      11
Lagrange multiplier rule      145
Lagrange multipliers      147 246 247 255
Lagrange problem      103
Lagrange variational problem      142 148 151 244
Lagrangian      117 142 143 146 148 151 152 154 155 157 160 162 164 165 167 168 170 171 174 183 185 187 219 220 224 225
Laplace operator      27
Laplace — Beltrami operator      386 393 398
Leaf      69 70
Lebesgue intergral      53
Left invariant      89
Left translation      88 93
Legendre condition      147 151
Levi form      423 425
Levi — Civita affine connection      273
Lie algebra      35 63 65 78 84 217 353
Lie algebra of vector fields      75 174 178
Lie algrebra of lie group      86
Lie derivative      10 18 40 41 46 47 106 354 396
Lie groups      26 34 70 81 175 342
Lie series      249
Lie subalgebra      65 74 91
Lie theory      73
Lie transformation group      82 94
Linear automorphism      94
Linear homogeneous differential equations      79
Linear lie algebra      78
Linear operator      85
Linear part of a vector field      379
Linear representation      82 88
Linear transformation      83
Local moving frame      321
Lorentz group      192 199 203 205 207 209 342
Lorentz metric      386
L’Hopit $\bar{a}$ l’s rule      306
Manifold      26 30 35 50
Mass      98 196
Matrix      15
Matrix, Riccati systems      77
Maximal connected integral submanifold      67 69 91
Maximal integral submanifold      126 127
Maximal point      64 65 345 346
Maximal rank mapping      29 32 58 158
Maximal subalgebra      78
Maxwell’s equations      201
Mayer variational problem      244
Mean      140
Mean curvature      391 392
Measure zero      57
Metric space      285 348
Metric structure      99
Michelson — Morley experiment      201
Minimal submanifold      331 332
Minkowskian geometry      195
Module      10 22 30 46
Moment of inertia      220

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