Авторизация
Поиск по указателям
M.A.Akivis, V.V.Goldberg — Projective Differential Geometry of Submanifolds
Обсудите книгу на научном форуме Нашли опечатку?
Название: Projective Differential Geometry of SubmanifoldsАвторы: M.A.Akivis, V.V.Goldberg Аннотация: In this book, the general theory of submanifolds in a multidimensional projective space is constructed. The topics dealt with include osculating spaces and fundamental forms of different orders, asymptotic and conjugate lines, submanifolds on the Grassmannians, different aspects of the normalization problems for submanifolds (with special emphasis given to a connection in the normal bundle) and the problem of algebraizability for different kinds of submanifolds, the geometry of hypersurfaces and hyperbands, etc. A series of special types of submanifolds with special projective structures are studied: submanifolds carrying a net of conjugate lines (in particular, conjugate systems), tangentially degenerate submanifolds, submanifolds with asymptotic and conjugate distributions etc. The method of moving frames and the apparatus of exterior differential forms are systematically used in the book and the results presented can be applied to the problems dealing with the linear subspaces or their generalizations.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1993Количество страниц: 362Добавлена в каталог: 11.12.2009Операции: Положить на полку |
Скопировать ссылку для форума | Скопировать ID
Предметный указатель
72 (0, 2)-tensor 214 215 232 (0, 3)-tensor 215 (r-1)-secant subspace 30 1-form, differential 8 1st canonical tensor 230 1st generalized Reiss theorem 272 1st integral 15 26 116 1st neighborhood of hyperband 257 1st normal(s) 174 250 1st normal(s) of hyperband 262 1st normal(s) of hypersurface 212 222 241 242 248 1st normal(s), invariant 230 1st normal(s), pencil of 231 250 1st normal(s), space of hypersurface 53 1st normal(s), subnormal of 174 175 193 1st normal(s), subspace 36 40 53—55 61 84 147 167 1st normal(s), subspace reduced 42 54 55 81 167 206 1st order frames 34 1st order frames, bundle of 93 1st order tangency 216 1st osculating subspace of submanifold 41 2-component conjugate system 165 169—171 2-component conjugate system, conic 169 2-component system of asymptotic distributions 148 2-component system of asymptotic distributions, complete 148 2-component system of asymptotic distributions, complete, doubly foliated 149 150 2-component system of asymptotic distributions, complete, integrable conjugate 169 2-dimensional conic submanifold 109 110 2-dimensional distribution 77 2-dimensional Grassmann 3-web 276 2-dimensional submanifold 59 64—66 158 207 289 2-dimensional submanifold of 4th order 30 2-dimensional submanifold, 2nd fundamental form of 59—61 64—66 158 289 2-dimensional submanifold, asymptotic direction of 60—61 64—66 2-dimensional submanifold, conjugate net of 60 2-dimensional submanifold, infinitesimal displacement of moving frame of 287 2-dimensional submanifold, invariant normalization of 207 2-dimensional submanifold, moving frame of 287 2-dimensional submanifold, osculating subspace of 289 290 2-dimensional submanifold, semi-asymptotic net of 61 2-dimensional submanifold, smooth 285 2-dimensional submanifold, tangent subspace to 290 2-dimensional submanifold, tangentially degenerate 67 2-dimensional submanifold, tangentially degenerate normalized 205 2-dimensional submanifold, Veronese mapping of 64—66 2-dimensional Veronese variety 67 285 290 295 2-plane(s) 21 59 70 137 272 291 2-plane(s), one-parameter family of 60 2-ruled submanifold 72 2-web 77 2-web, curvilinear 77 2-web, quadrilateral 77 2nd fundamental form(s) of conjugate net 74 2nd fundamental form(s) of hyperband 258 2nd fundamental form(s) of hypersurface 53 210 212 244 272—275 277 278 291 2nd fundamental form(s) of image of the Grassmannian 51 2nd fundamental form(s) of Laplace transform 98 2nd fundamental form(s) of Segre variety 41 158 2nd fundamental form(s) of submanifold 40 42 47 62 71 165 169 277 2nd fundamental form(s) of submanifold, 2-dimensional 59—61 64—66 289 2nd fundamental form(s) of submanifold, 3-dimensional 56—58 67—70 2nd fundamental form(s) of submanifold, carrying conjugate net 73 2nd fundamental form(s) of surface 91 92 2nd fundamental form(s) of Veronese variety 41 287 2nd fundamental form(s), parallel vi 221 222 2nd fundamental form(s), parallelism of 221 2nd fundamental form(s), pencil of 57 2nd fundamental form(s), system of 64—70 169 2nd fundamental tensor of hypersurface 54 218 221 2nd fundamental tensor of hypersurface, covariant differential of 221 2nd fundamental tensor of hypersurface, indefinite 226 2nd fundamental tensor of hypersurface, parallelism of 221 2nd fundamental tensor of hypersurface, positive definite 226 242 2nd fundamental tensor of hypersurface, rank of 54 2nd fundamental tensor of submanifold 39 73 148 149 152 165 269 277 2nd fundamental tensor of submanifold, rank of 56 2nd generalized Reiss theorem 277 2nd Laplace transform 101 2nd neighborhood of hypersurface 233 2nd normal(s) 174 2nd normal(s) of hyperband 262 2nd normal(s) of hyperguadric 177 2nd normal(s) of hypersurface 212 222 224 241 242 248 2nd normal(s), invariant 230 2nd normal(s), pencil of 231 2nd normal(s), subspace 42 45 2nd normal(s), subspace, basis of 43 2nd normal(s), subspace, dimension of 43 2nd normal(s), subspace, reduced 45 81 2nd order, asymptotic direction 48 57 63 71 92 94 145 2nd order, asymptotic direction of 2-submanifold 60—61 64—66 2nd order, asymptotic direction of 3-submanifold 57—58 67—70 2nd order, asymptotic direction on hypersurface 230 2nd order, cone 215 2nd order, conjugate directions 49 57 63 2nd order, curve 31 269 2nd order, frame 42 2nd order, neighborhood of hyperband 257 259 260 2nd order, tangency 211 216 2nd osculating subspace 41 42 47 55 56 61 62 82 85 145 147—150 152 165 167 2nd osculating subspace of 119 120 124 127 128 2nd osculating subspace of conjugate net 75 2nd osculating subspace of image of Grassmannian 51 2nd osculating subspace of Segre variety 41 2nd osculating subspace of Veronese variety 42 2nd polar 215 3-conjugate system R 111 3-dimensional projective space 209 3-dimensional Riemannian space of constant curvature 135 3-dimensional submanifold 56—58 72 3-dimensional submanifold, 2nd fundamental form of 56—61 3-dimensional submanifold, asymptotic direction of 57—58 67—70 3-dimensional submanifold, carrying net of asymptotic lines 151 3-dimensional submanifold, conjugate directions of 57—58 67—70 3-dimensional submanifold, conjugate net of 57 3-dimensional submanifold, with 6-dimensional osculating subspace 72 3-dimensional submanifold, with complete system of one-dimensional asymptotic distributions 151 3-plane 56 156 3-web, Grassmann 275 3-web, Grassmann, 2-dimensional 276 3-web, Grassmann, curvature tensor of 275 3-web, Grassmann, GW(3,2,1) 275 276 3-web, Grassmann, GW(3,2,r) 275 276 3-web, Grassmann, hexagonal 275 276 3-web, rectilinear 275 3-web, rectilinear, hexagonal 276 3rd class curve 276 3rd fundamental form 44 49 153 3rd fundamental form of submanifold with conjugate net 75 3rd fundamental tensor 44 152 3rd order conjugate directions 50 71 87 111 3rd order curve 276 3rd order frame 238 241 3rd order frame subbundle 235 237 3rd order neighborhood of hyperband 260 264 3rd order neighborhood of hypersurface 211 225 227 233 3rd order tangency 217 218 220 3rd osculating subspace 45 154 4th harmonic point 61 4th neighborhood of hyperband 262 265 4th neighborhood of hypersurface 212 213 224 233 242 4th neighborhood of submanifold 199 4th order curve 30 4th order curve, 2-submanifold 30 4th order curve, frame 240—242 4th order curve, fundamental object 242 4th order curve, subbundle 237 5-dimensional submanifold 72 5th neighborhood of hypersurface 232 233 241 242 5th order fundamental object 241 244 Abel 270 295 297 Abel, condition 279 Abel, theorem 270 278 295 Abel, theorem, generalization of 295 Absolute of 134 Absolute, differential invariant 214 233 Absolute, invariant 4 227 231 250 Absolutely invariant form 233 250 Admissible transformation 61 35 39 74 174 179 183 185 200 212 Affine, connection 16 17 184 Affine, connection in normal bundle 183 Affine, connection in tangent bundle 179 183 193 Affine, connection on hypersurface 221 Affine, connection, curvature tensor of 17 179 Affine, connection, torsion tensor of 17 179 Affine, connection, torsion-free 17 Affine, coordinate system 276 Affine, frame 21 22 Affine, geometry vi 221 Affine, normal vi 224 268 Affine, normalization 177 180 185 Affine, space 21 173 206 224 266 Affine, space, infinitesimal displacement of frame of 21 Affine, space, structure equations of 22 Affine, space, transformation of 21 Affinor 242 Akivis 61 70 72 82 101 111 112 141 169 171 172 205 207 212 277 282 296—300 Algebraic, cone 130 Algebraic, curve 270 Algebraic, equation vi 94 95 99 204 Algebraic, family of hyperplanes 119 Algebraic, geometry v Algebraic, homogeneous polynomial 195 Algebraic, hypersurface 122 272 278 Algebraic, manifold 269 Algebraic, variety v 26 117 129 261 Algebraic, variety, projective 278 Algebraizability condition 269 Algebraizability condition for hyperdistribution 282 Algebraizable Grassmann d-web 276 Algebraization problem 269 278 279 Algebraization problem for multidimensional webs 296 Algebraization problem for submanifolds 296 Alternated Ricci tensor 185 Alternation 27 Analytic function 7 Analytic manifold 5 Anti-commutative 8 Apolar tensors 214 233 Apolarity 213—216 228 233 259 265 Arbitrariness of general integral element 13 Asymptotic, cone(s) 47 Asymptotic, cone(s) of 2nd order of hypersurface 210 Asymptotic, cone(s) of image of Grassmannian 51 53 Asymptotic, cone(s) of order q 48 Asymptotic, cone(s), filtration of 49 53 Asymptotic, curve 47 54 145 171 Asymptotic, curve of 2nd order 48 Asymptotic, curve of hyperdistribution 281 282 Asymptotic, curve of hypersurface 211 Asymptotic, curve of manifold of hypercones 284 Asymptotic, curve of Monge equation 281 Asymptotic, curve of order q 48 71 Asymptotic, curve of surface 251 Asymptotic, curve, rectilinear 155 158 159 Asymptotic, direction of 2-submanifold 60—61 64—66 Asymptotic, direction of 2nd order 48 57 63 71 92 94 145 Asymptotic, direction of 3-submanifold 57—58 67—70 Asymptotic, direction of image of Grassmannian 53 Asymptotic, direction of order q 48 71 Asymptotic, direction on hypersurface 230 Asymptotic, direction, double 66 70 Asymptotic, direction, real 67 Asymptotic, direction, threefold 69 Asymptotic, distribution 145 171 Asymptotic, distribution, complete 2-component 148 Asymptotic, distribution, complete multicomponent 150 171 Asymptotic, distribution, integrable 145 Asymptotic, distribution, one-dimensional 161 Asymptotic, holonomic net 155 Asymptotic, hypercone 279—284 Asymptotic, subspace 145 147 Atanasyan 205—207 300 AutoDual 117 255 Autodual, hyperband 255 256 Autodual, pair 255 Autodual, tangentially degenerate submanifold 117 255 Autopolar simplex 23 Axial, normalisation 205 Axial, plane 111 Axial, point 55 65 127 Axis of Koenigs net 170 Baecklund 295 301 Baimuratov 57 72 171 296 300 301 Balazyuk 321 Baldasari 72 301 Band 268 Barner vii 171 301 Base of bundle of 1st order frames 35 Base of connection 178 Base of normal bundle 182 Base of subbundle 24 Base, form 14 35 Base, natural 14 Basis of 2nd normal subspace 43 Basis of cotangent space 6 19 Basis of hyperplane 131 Basis of tangent space 19 Basis of vector space 1 35 Basis, dual 5 Basis, form 35 Basis, form of Grassmannian 38 128 Basis, form of hypersurface 210 244 Bazylev 82 111 112 206 301 302 Bell 111 302 Berezina 207 302 Bertini 302 Bijective mapping 7 Bilinear equation 223 Bilinear form 49 132 Bisecant 29 Bisecant, variety 29 31 285 286 Bisecant, variety, degenerate 285 286 BLANK 112 302 Blaschke 72 259 268 302 303 Blaschke affine normal vi 224 268 Bol v 72 209 303 Bompiani 71 72 296 303 Borisenko 134 141 303 Bortolotti v 266 303 Botsu 275 295 303 Brauner v 141 304 Bryant 304 Bubyakin 70 304 Bundle of 1st order frames 35 93 Bundle of 1st order frames, base of 35 Bundle of 1st order frames, typical fiber of 35 Bundle of 2nd fundamental forms 40 Bundle of 2nd fundamental forms, dimension of 40 Bundle of 3rd fundamental forms 44 Bundle of 3rd fundamental forms, dimension of 45 Bundle of hyperplanes 121 122 127 189 Bundle of hyperplanes, center of 121 122 189 Bundle of planes 176 Bundle of straight lines 275 Bundle of subspaces 28 Bundle, cotangent 19 Bundle, frame 5 16 Bundle, frame, dimension of 5
Реклама
-ruled submanifold 
|
|
О проекте