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| Alekseevskij D.V., Vinogradov A.M., Lychagin V.V. — Geometry I: Basic Ideas and Concepts of Differential Geometry |
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Название: Geometry I: Basic Ideas and Concepts of Differential Geometry
Авторы: Alekseevskij D.V., Vinogradov A.M., Lychagin V.V.
Язык: 
Рубрика: Математика/
Статус предметного указателя: Готов указатель с номерами страниц
ed2k:
Год издания: 1991
Количество страниц: 264
Добавлена в каталог: 02.05.2008
Операции: Положить на полку |
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| Предметный указатель |
Homogeneous harmonic map 200
Homogeneous Riemannian manifold 106
Homogeneous space 97
Homogeneous symplectic manifold 111
Homomorphism 155
Hopf, H. 76
Horizontal distribution 159
Horizontal lift 159 160
Horizontal space 159
Horizontal subspace 160
Hyper — Kahlerian manifold 84
Hyperbolic differential equation 144
Imprimitive smooth action of a group 100
Index of a handle 220
Index of a point  220
Index of an operator 229
Induced bundle 59
Infinitesimal bending of a surface 201
Infinitesimal coordinate system at a point 149
Infinitesimal deformation 239
Infinitesimal gauge transformation 161
Infinitesimal holonomy algebra 83
Infinitesimal operator of parallel transfer 33
Infinitesimal Stokes formula 71
Infinitesimal symmetry 124
Infinitesimal symmetry transformation 191
Infinitesimal transformation 191
Infinitesimally homogeneous geometric structure 237
Inner symmetry of a differential equation 131 136
Integrability problem 182
Integrable  -structure 182
Integral submanifold 119 126
Integral subspace 143
Intrinsic curvature 28
Intrinsic geometry of surfaces 30
Intrinsically equivalent systems of differential equations 136
Involution 143
Involutive differential equation 130
Involutivity in Cartan’s sense 145
Involutivity in Spencer’s sense 141
Irreducible pseudogroup 194
Irreducible Riemannian manifold 82
Isometric embedding 205
Isomorphism of bundles 59 155
Isotropic subspace 128
Isotropy group of a pseudogroup 193
Isotropy representation 99
Isotropy representationof order  99 193
Jacobi field 216
Jacobi matrix 74
Janet, M. 204
Jessen, B. 241
Jordan, M.F. 195
K hler form 84
Khler — Einstein metric 243
Khler, E. 83 189
Khlerian manifold 84
Kac, M. 245
Kaluza, T. 153
Kerr, R.R. 180
Killing field 179 180
Killing, W. 48 77 107 180
Klein, F. 18 92 94 95 111 114 131 157
Klein,O. 153
Kodaira, K. 233
Kovalevskaya, S.V. 142
Kuiper, N.H. 205
Lagrange bracket 123
Lagrange, J.L. 123 145
Laplace, P.S. 244
Left translation 89
Left-invariant operator 89
Legendre transformation 121
Legendre, A.M. 122
Leibniz rule 61
Leibniz, G.W. 61
Lens space 155
Levi — Civita connection 73
Levi — Civita, T. 73 87 166
Lewy, H. 189 201
Lie algebra 93 97
Lie algebra of infinitesimal gauge transformations 161
Lie derivative 69
Lie equation 191
Lie field 135
Lie group 93 96
Lie pseudogroup 190
Lie transformation 135
Lie, S. 18 93 94 119 131 135 177
Liebmann, H. 200
Linear action of a group 97
Linear connection 72
Linear geometric structure of type  151
Linear Lie equation 191
Linear representation 97
Liouville, J. 217
Lobachevskij, N.I. 18 50 82 93 202
Local coordinate system 55
Local coordinates 29
Local equivalence of differential equations 125
Local equivalence of manifolds with linear connections 76
Locally effective action of a group 97
Locally effective systems of differential equations 1 36
Locally equivalent manifolds 76
Locally Euclidean manifold 78
Locally isometric Riemannian manifold 178
Locally isomorphic Lie groups 96
Locally maximal submanifold 126
Locally rigid surface 48
Locally symmetric Riemannian manifold 83
Locally symmetric space 104
Lomonosov, M.V. 9
Lorentz, H.A. 244
Lorentzian manifold 71
Lorentzian metric 71
Lyusternik, L.A. 199
M bius, A.F. 58
Mainardi, G. 37—40
Manifold 56
Manifold with boundary 57
Margulis, G.A. 236
Maurer — Cartan equation 164
Maurer, W.A. 164
Maxwell, J. 52 149 154 177
McKean, H. 246
Mean curvature 31 47
Mendeleev, D.I. 93
Metrical invariant 26
Metrically equivalent curves 25
Mills, R.L. 166 167
Milnor, J. 58 217 247
Minakshisundaram, S. 246 247
Minding, F. 200
Minimal geodesic 76
Minimal surface 206
Minkowski metric 71
Minkowski, H. 52 71 241 242
Minkowski’s problem 241
Mixed tensor 65
Moduli space 235
Monge axis 117
Monge cone 116
Monge — Amp re equation 241
Monge, G. 114 241
Morphism of maps 59
Morrey, C. 207
Morse, M. 200 219 222
Moser, J. 204
Mostow, G.D. 236
Moving frame method 25 28
| Multivalued solution of an equation 120 133
Nash, J. 204 205
Natural connection 104
Natural field quantity 153
Natural parameter 25
Naturally reductive space 107
Naturalness of an outer differential 70
Newlander, A. 186
Nijenhuis algebra 238
Nijenhuis algebraic bracket 238
Nijenhuis differential bracket 238
Nijenhuis tensor 186
Nijenhuis, A 186 237—240
Nirenberg, L. 186
Noether, M 236
Noether’s formula 234
Nomizu map 101
Nomizu operator 101
Nomizu, K. 101 106
Non-degenerate Poissonian structure 89
Normal connection 42
Normal coordinates 75
Normal curvature of a surface 31
Normal Riemannian coordinates 75
Normal section 31
Normal space 171
Normal tensor of a connection 75
Ochiai, T. 196
One-parameter group 62
Operation of parallel transport 34
Order of a -structure 156
Order of a homogeneous space 99
Ordinary integral subspace 143
Oriented geodesic curvature 35
Oriented volume 27
Orthogonal transformation 96
Osculating space 26
Outer symmetry of a differential equation 131 136
Oval 197
Oval hypersurface 241
Oval surface 198
Parallel tensor field 74
Parallel transport 34 73 160 164
Parametrized curve 25
Parametrized surface 29
Partial Legendre transformation 121
Patodi, V.K. 244
Peijel, A. 245—247
Peterson operator 3 1
Peterson, M.K. 32 38 40
Pfaff system 142
Pfaff, J.F. 119 136 142
Pfaffs problem 136
Pfaflian of a matrix 226
Plateau, J. 206
Pogorelov, A.V. 201 242
Poincar , H. 18 199 200 233
Poincar’s lemma 71
Point transformation 135
Poisson, S.D. 88 89
Poissonian centre 89
Poissonian fibration 89
Poissonian fibres 89
Poissonian manifold 89
Poissonian structure 89
Polar system 143
Pontryagin class 228
Pontryagin, L.S. 221
Praismann, A. 219
Primitive pseudogroup 194
Primitive smooth action of a group 100
Principal -bundle 154
Principal bundle 1 54
Principal curvatures 31 47
Principal directions 31 47
Principal linear part 61
Principal of  invariants 184
Principle of extension 101
Projective connection 95
Prolongation of a -structure 186 188
Prolongation of a differential equation 137 171
Prolongation of a differential operator 172
Prolongation of a Lie algebra 188
Prolongation of a symbol 140
Pseudo — Riemannian manifold 71
Pseudogroup 190
Pythagoras 14 92
Quaternion manifold 84
Quotient equation 147
Rad , T. 206
Rashevskij, P.K. 103 159
Rate of deformation tensor 70
Rate of rotation of the tangent 26
Reductive decomposition 102
Reductive homogeneous space 102
Regular equation 130 138
Regular integral subspace 143
Regular point 125 130 144
Regular point of a Pfaff system 142
Regular subspace 143
Regularity of a curve 25
Reifenberg, E.R. 207
Restricted holonomy group 82
Rham, C.de 17 82 148 209
Ricci curvature 80
Ricci operator 79
Ricci tensor 79
Ricci, G. 43 45 49 79
Richardson, R.W. 239
Riemann relation 234
Riemann — Roch — Hirzebruch formula 234
Riemann, G.F.B. 23 28 50—52 81 92 231
Riemannian manifold 71
Rigid system of differential equations 136
Rigidity 201
Rinow, W. 76
Roch, E. 231
Rokhlin, V.A. 204
Rozendorn, E.R. 205
Scalar curvature 79
Schlfli, L. 204
Schouten, J.A. 80
Schur, F. 81
Schwarz, H.A. 206
Second Bianchi identity 83
Second quadratic form 30 42
Section of a bundle 54
Sectional curvature 81
Self-dual components of a Weyl tensor 81
Serre duality 240
Serre, J. — P. 145 233
Shift form 156
Shift form of a -structure 157
Shift transformation 62
Shnirel’man, L.G. 199
Shoen, S. — T. 219
Shortest curves 42
Signature of a metric 71
Simons, J. 200 208
Simple bivector 46
Singer, I.M. 83 163 225 230 231 246
Singular integral subspace 143
Singular point 125 130 220
Singular point of a Pfaff system 142
Skew-symmetric tensor 66
Smith, F. 200
Smooth action of a group 97
Smooth atlas 56
Smooth bundle 58
Smooth function 55 146
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