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Alekseevskij D.V., Vinogradov A.M., Lychagin V.V. — Geometry I: Basic Ideas and Concepts of Differential Geometry
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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 264

Добавлена в каталог: 02.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $a$      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 $G$-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 $k$      99 193
Jacobi field      216
Jacobi matrix      74
Janet, M.      204
Jessen, B.      241
Jordan, M.F.      195
K$\ddot{a}$hler form      84
K$\ddot{a}$hler — Einstein metric      243
K$\ddot{a}$hler, E.      83 189
K$\ddot{a}$hlerian 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 $W$      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$\ddot{o}$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$\grave{e}$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 $G$-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$\acute{e}$, H.      18 199 200 233
Poincar$\acute{e}$’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 $G$-bundle      154
Principal bundle      1 54
Principal curvatures      31 47
Principal directions      31 47
Principal linear part      61
Principal of $n$ invariants      184
Principle of extension      101
Projective connection      95
Prolongation of a $G$-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$\acute{o}$, 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
Schl$\ddot{a}$fli, 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 $G$-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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