|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Alekseevskij D.V., Vinogradov A.M., Lychagin V.V. — Geometry I: Basic Ideas and Concepts of Differential Geometry |
Обсудите книгу на
Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter
|
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 |
Скопировать ссылку для форума | Скопировать ID
|
|
|
| Предметный указатель |
 -equivalent submanifolds 167
-jet of a map at a point 169
-jet of a section 169
-jet of a submanifold at a point 167
 -plane 134
 -characteristic of a bundle 234
 -equivalent submanifolds 218
 -field 148
-map 147
 -genus of a manifold 234
( ,  )-form 232
1-jet 115 116
3-web 175
Action of a group 96
Acyclic system of differential equations 141
Adjoint action of a group 98
Adjoint representation of an algebra 98
Affine equivalence 27
Affine geometric structure 151
Affine invariant 27
Affine symmetric manifold 104
Affine transformation 27
Aleksandrov, A.D. 201 241
Allendorfer, C.B. 49
Almgren, F.G. 207
Almost complex structure 84 152
Alternation 67
Ambrose, W. 83 163
Ample canonical bundle 243
Analytic system of differential equations 142
Anti-self-dual components of a Weyl tensor 81
Arithmetic genus of a manifold 234
Atiyah, M. 225 230 244
Backlund, A.V. 135
Basic equations 44
Beez, R. 48
Beltrami — Laplace operator 87 212
Beltrami, E. 18 87 202
Berezin, F.A. 237
Berger, E. 205
Berger, M. 83 110
Bernstein, S.N. 208
Betti numbers 209
Bianchi, L. 46
Bieberbach, L. 235
Bivector 46
Blanu a, D. 205
Blaschke, W. 201
Blecker, D. 247
Bochner, S. 205 214
Bol, G. 198
Bolyai, J. 18 202
Bombieri, E. 208
Bonnet, O. 28 35 37 224
Bordancy 223
Bordant surfaces 224
Borel, A. 138
Bott, R. 223 244
Boundary of a manifold 57
Bourbaki, N. 10
Brieskorn, E. 58
Bryant, R. 205
Bundle associated with a principal bundle 158
Bundle of geometric quantities 158
Burgers, W. 148
Burstin, I.L. 204
Calabi, E. 241 243
Calabi’s conjecture 243
Canonical bundle 243
Canonical connection 102
Carath odory, C. 198
Cartan distribution 133 147 168
Cartan plane 147 168
Cartan structure equation 163
Cartan, E. 77 92 144 145 189 194 196 204 209
Cauchy data 124 130
Cauchy, A. 123
Central symmetry 104
Character of a Pfaff system 143
Characteristic 116 117 129
Characteristic class 28 228
Characteristic class of a manifold 228
Characteristic curve 117
Characteristic field 117 125
Characteristic manifold 129
Chart 29 55
Chern character 230
Chern characteristic class 228
Chern, S.S. 227 230
Christoffel of the normal connection 42
Christoffel symbols 32 41 72
Christoffel, E.B. 32
Clairaut, A.C. 121
Class of a distribution 128
Classical simple Lie group 96
Closed differential form 71
Closed set 57
Closed subgroup 99
Clothed surface 224
Codazzi, D. 38—40
Codimension of a distribution 126
Coframe of order 150
Cohn — Vossen, St 201
Cohomologies of a Lie algebra 239
Commutator of a vector field 43
Compactness 57
Complete system of metric invariants 27
Complete vector field 62
Completely integrable distribution 127
Complex local coordinates 231
Complex manifold 231
Complex pseudogroup 190
Components of a covector 64
Components of a tensor 44
Configuration 54
Conformal metric 95
Conformal model 82
Conjugate points 216
Connection 35
Connection form 161
Connection in a principal  -bundle 160
Contact Hamiltonian 123
Contact structure 125
Contact transformation 121
Contact vector field 122
Contravariant tensor 65
Contravariant valency 65
Convolution operation 66
Cosmological constant 80
Cotangent bundle 64
Cotangent space 64
Courant, R 206
Covariant derivative 41 72 164
Covariant differential 74 163 164
Covariant differentiation 33
Covariant differentiation along  33
Covariant differentiation of a normal field 42
Covariant tensor 65
Covariant valency 65
Covariantly constant tensor field 74
Covector field 64
Covering 155
Critical value of a function 220
Curvature 26
Curvature tensor of a linear connection 78
Curvature tensor of a normal connection 45
Curvature tensor of a surface 44
Curvature, two-form of a connection 162
Curvilinear coordinates 29
Darboux, G. 28 38 1 1 1 128 129 241
| De Rham cohomologies 209
de Rham complex 209
Deficiency of a loop 35
Deformed cohomologies 240
Deformed complex 240
Derivation formulae 43
Descartes, R. 14—16
Development of a curve 34
Diffeomorphism 58
Differential equation 133
Differential equation of order on submanifolds 171
Differential form of degree 68
Differential form of the first degree 21 64
Differential form on  147
Differential group of order 1 50
Differential invariant 25 183
Differential of a function 64
Differential of an algebra  with values in the -module 20
Differential operator 85 171
Differentially closed ideal 146
Dimension of a distribution 126
Dirac, P.A.M. 153
Distribution on a smooth manifold 126
Dolbeault cohomologies 232
Dolbeault cohomologies of a holomorphic bundle 233
Dolbeault cohomologies with values in a bundle 233
Dolbeault complex 232
Dolbeault, P. 231—233
Douglas, J. 206
Effective action of a group 97
Effective subalgebra 99
Efimov, N.V. 202 203
Einstein space 80
Einstein, A. 28 40 52 81 234
Elliptic G-structure 188
Equation of principal type 142
Equation soluble at a point 130
Equivalence of bundles 59
Equivalence problem 180
Equivalent atlases 56
Equivalent equations 128
Equivalent smooth structures 58
Euclid 14 15 93
Euclidean metric 235
Euler class 228
Euler class transformation 121
Euler, L. 121 228 229
Exact differential form 71
Exceptional Lie group 96
Exponential map 75
Extension of a tensor at a point 76
Exterior algebra 67
Exterior product 67
Faltings, G. 17
Federer, L. 207
Feldmann 198 199
Fenchel, W. 241
Fermat, P. 14—16
Field of geometric quantities of order 1 151
Field of geometric quantities of type  151
Field of parallel vectors along a curve 34 41 73
Field of tangent vectors of order k 152
Field quantity 52
First Bianchi identity 46 79 163
First quadratic form 29 40
Flat -structure 188
Flat connection 78 162
Flat geometric structure 181
Flat section 181
Flow 62
Fomenko, A.T. 208
Form of the first kind 234
Formally integrable -structure 188
Formally integrable differential equation 138 171
Formally integrable system of differential equations 138
Fr licher, A. 240
Frame of order 149
Free action of a group 154
Frenet formula 27
Frenet frames 26
Frenet, J.F. 26
Frenkel, T.T. 208
Frobenius, F. 128 186
Full linear group 96
G$-structure 152
G$-structure of finite type 188
Gaffney, P.W. 247
Galois group 93
Galois, E. 93 94
Gauge transformation 155
Gauge vector field 161
Gauss, C.F. 28 37—40 50 5 1 202
Gaussian curvature 28 31 47
Gaussian curvature form 226
Gaussian map 36 228 241
Gel’fand, I.M. 229
Generalized -structure 157
Generating function 123
Generating function of a contact transformation 122
Generating function of a higher symmetry 148
Genre of a Pfaff system 144
Geodesic 42 73
Geodesic curvature 32 42
Geodesic curvature vector 32
Geodesic curve 32
Geodesics of a Riemannian manifold 73
Geometric quantity of type 151 158
Geometrical curve 25
Geometrical structure of type 158
Giorgi, E.de 208
Giusti, M. 208
Global Gauss — Bonnet formula 37
Globalizable pseudogroup 190
Goldschmidt, H. 141
Graded Lie superalgebra 237
Gradient of a function 178
Grassmann algebra 67 68
Grassmann bundle 159
Grassmann manifold 109
Grassmann, H.G. 152
Green, R.E. 20
Griffiths, P. 24 205
Gromov, M.L. 204 217 219
Group of unimodular transformations 96
Group structure 236
Guillemin, V. 189 195
Halphen, G. — H. 177
Hamburger, H. 198
Hamiltonian 88
Hamiltonian group of automorphisms 111
Hamiltonian vector field 89
Handle of given index 220
Harmonic form 166 233
Heisenberg, W. 154
Herglotz, G. 201
Higher curvature of a curve 27
Higher infinitesimal symmetry of a differential equation 148
Higher symmetry of a differential equation 147
Hilbert, D. 202 203
Hirzebruch, F. 225 231
Hitchin, N. 81
Hodge, W.V.D. 211
Holomorphic form 232
Holomorphic tangent bundle 233
Holomorphic vector bundle 232
Holonomy algebra 83
Holonomy algebra of a linear connection 82
Holonomy algebra of a Riemannian manifold 82
Holonomy group 82 162
Homogeneous Hamiltonian manifold 111
|
|
|
| Реклама |
|
|
|
|
|
О проекте