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

Momentum      100 207
Momentum, space      176
Monge system      254 255
Morse index theorem      401 419
Moving frames      26 383 384
Multilinear      11
Multiple integral      113
Negatively oriented coordinate system      50
Newtonian mechanics      185 186 190 192 195
Newton’s equations      427
Newton’s equations of motion      100 151
Newton’s law of motion      98 155
Nilpotents      95
Nonholonomic      151
Nonsingular points      57
Normal bundle      343
Normal vector bundle      318
Number theory      71
Observables      178 179
One parameter group      38 39 44 48 94 159 248
One parameter subgroup      82 353
Operator power series      83
Optimal control      151 256
Optimality      145
Orbit      83 93 178 229 343 344 346 351
Orbit space      347 349
Ordinary differential equations      38
Orientable      50 57
Orientation      50
Oriented manifold      60 62
Orthogonal group      218
orthogonal matrices      96
Orthogonal matrix      217
Orthogonal transformations      156
Osculating space      381
Paralle translation      264 265 270 359
Partial differential equations      59
Particle      98
Partition of unity      50 52 61 70
Path      241 277 279
Path, system      241 249
Periodic      139
permutations      81
Perpendicular      164 167 173
Perpetual motion machine      244
Perturbation      139
Perturbation theory      139
Peter — Weyl theorem      208
Pfaffian equation      243 254 255
Phase space      176 178 179 242
Plancherel theorem      208
Planck’s constant      136
Poincar $\acute{e}$ lemma      176
Poincar $\acute{e}$ — Birkhoff fixed point theorem      182
Point set topology      6
Poisson bracket      176—178 231
Polar coordinates      27
Positive orientation      60
Positive oriented coordinate system      50
potential energy      99
Power series      83 85
Principal axes      220
Principal curvature      325 365
Principal point      345 346
Principle of least action      136
Principle of Maupertuis      188 190
Projection      93
Projective space      359
Prolonged vector field      158
Proper map      85
Pseudo — Riemannian manifold      392 397 400
Pseudo — Riemannian metric      195 272
Pseudoconvexity      425 426
Quadrature      43 75 227
Quantum field theory      9
quantum mechanics      81 136 179 188
R $\acute{e}$ p $\grave{e}$ re mobile      321
Rational lie algebra      84
Rauch comparison theorem      313
Ray(s)      144 168 172 201
Real Lie algebra      84
Regular Variational problem      155 161 162 173 186
Regularly imbedded submanifold      70 71 343 344 351
Relativity      272
Riccati—Equation      44
Ricci curvature      305
Ricci identity      302 358

Ricci tensor      299 300
Riemann integral      51 53 58 60
Riemannian affine connection      272—275
Riemannian connection      273 274 321 323
Riemannian geometry      257 261
Riemannian metric or manifold      27 165 191 261 272 275 277 280 287 289 292 294 297 308 310 312 318 322 331 342 349 362 420
Riemannian space      228
Right invariant      89
Right translation      88
Rigid body      109 172 216 217 219 221 223 232 429
Rigidly related submanifolds      366
Ring      8
Routhian      215
Sard’s theorem      331
Scalar field      3
Scalar potential      185 186
Schwarz inequality      279 280
Second fundamental form      319 320 326 333 335 337 338 363 373 376 382 384 425
Second variation      117 257
Second variation formula      119 121 291 295 325 327 335
Sectional curvature      302 305 308 316 337
Self-parallel curves      265
Semigroups      180
Simply connected      181 270 290
Singularities of mappings      54
Skew symmetric      17
Skew symmetric matrices      96
Slice      69 70
Soap bubbles      332
solvable      214
Special relativity      203 208 342
Sphere      23 230
Spherical harmonics      208 389 390
Stokes’ formula      57 60 113 114 116 392
Stokes’ Theorem      107
Stress tensor      107
Structure coefficients      220
Sturm comparison theorem      315
Sturm — Liouville theory      401
Subgroup      92
Submanifolds      28 58 65
Submanifolds, map      30 69
Sum of one-parameter subgroups      87
Summation convention      21 336
Sun      140
Surface area      332
Symmetric space      358 359
Symmetric spaces      227 228
Symmetry(ies)      73 170 174 184 185 187
Tangent bundle      7 24 63 89 152
Tangent space      8 9 114
Tangent vector      7 8 17 19 24 152
Taylor’s expansion      86
Taylor’s formula for covariant derivatives      310
Tensor algebra      11
Tensor analysis      4 14 21 26 262
Tensor field      373 378
Thermodynamics      254
Top      226
Topological groups      81 345 349
Topological groups theory      72
Topological vector space      82
topology      23
Torsion      266
Torsion tensor      374 381
Total angular momentum      223 233
Total energy      99 103
Totally geodesic submanifold      337 338 339 340 351 352 365 375 381
Transformation group      81 87 93 354
Transition function      382
Transversal      116 120
Transversal geodesic      350
Transversal Jacobi field      330
Vector analysis      3 62 98
Vector bundle      9 11
Vector field      3 10 19 22 24 27 34 35 39 43 46
Vector field system      63 68
Vector potential      185 186
Vector product      3
Vector space      6 11 20 401
Velocity      196 199 201 203 204 208
Volume element      14 19 58
Volume element form      54
Volume forces      107
Wave      168
Wave equation      202
Wave fronts      144 201

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