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M.A.Akivis, V.V.Goldberg — Projective Differential Geometry of Submanifolds
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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 |
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Предметный указатель
Theorem, Frobenius 11 15 24 77 115 144 187 Theorem, Graf — Sauer 276 295 Theorem, Reiss 270 271 278 295 Theorem, Reiss, 1st generalized 272 Theorem, Reiss, 2nd generalized 277 Theorem, Segre 56 59 122 127 259 Theorem, Segre's type 71 111 Theorem, Segre, generalized 81—82 85 111 128 202 Theorem, Togliatti 72 Theorem, Vieta 204 276 Theory of curves 269 Threefold, asymptotic direction 69 Threefold, pair of conjugate directions 66 Togliatti 327 Togliatti, theorem 72 Torse 52 55 56 60 95 100 116 118 135 137 Torse, edge of regression of 100 118 Torsion, geodesic 205 Torsion, tensor of affine connection 17 179 Torsion-free, affine connection 17 Torsion-free, projective connection 205 Torsion-free, projective connection, curvature tensor of 205 Total differential 21 105 176 186 Trace of tensor 225 Trace-free part of quasitensor 183 Transformation by focal family of rays 94 112 Transformation by focal family of rays of submanifold of codimension 3 101 Transformation of affine space 21 Transformation of basis 63 Transformation, admissible 16 35 39 74 174 179 183 185 200 212 Transformation, centroprojective 74 Transformation, correlative 116 117 123 255 275 276 Transformation, Egorov vi Transformation, elliptic 23 Transformation, geodesic 180 Transformation, identity 1 18 Transformation, infinitesimal of frame 1 Transformation, invertible 5 Transformation, isotropy 22 Transformation, linear 18 Transformation, projective 18 240 243 244 254 Transformation, symmetric double 62 Trilinear form 50 Trushin 71 111 327 Typical fiber of bundle of 1st order frames 35 Typical fiber of connection 178 Tzitzeika v 327 Udalov 206 328 Unity point 18 Value of exterior p-form 9 van der Waerden — Bortolotti operator 184 Vangeldere v 72 112 328 Vanhecke 221 307 Vaona v 71 329 Variety, algebraic v 26 117 129 261 Variety, algebraic, projective 278 Variety, bisecant 29 31 285 286 Variety, bisecant, degenerate 285 286 Variety, Cartan 83 84 111 207 Variety, Cartan, invariant normalization of 207 Variety, focus 117 120 121 123 126 129 132 134 166 168 175 177 183 194 261 Variety, focus of 1st normal of 175 188 189 Variety, focus of generator 166 Variety, focus, degenerate 118 Variety, focus, equation of 122 Variety, focus, imaginary 137 Variety, focus, real part of 134 Variety, Monge 279 280 296 Variety, Monge, degenerate 279—281 Variety, Monge, nondegenerate 280 Variety, Segre 29 34 37 41 51 52 71—72 150 158 Variety, Segre, 2nd fundamental form of 41 158 Variety, Segre, dimension of 37 Variety, Segre, moving frame of 37 Variety, Segre, plane generator of 29 51 Variety, Segre, projection of 150 Variety, Segre, tangent subspace to 37 Vasilyan 256 259 268 328 Vasilyev v 328 Vector(s), collinear 17 18 290 Vector(s), conjugate 215 216 Vector(s), differential equations of 3 Vector(s), fields vii Vector(s), fields in involution 9 Vector(s), harmonic conjugate 267 Vector(s), law transformation of 3 Vector(s), relative 4 Vector(s), space 1 8 17 131 214 227 Vector(s), space infinitesimal displacement of frame of 2 Vector(s), space, basis of 1 35 Vector(s), tangent 5 Vector(s), tangent, coordinates of 14 48 Vectorial frame 18 Verbitsky 267 328 Veronese, embedding 296 Veronese, mapping 62—72 Veronese, mapping of 2-submanifold 64—66 Veronese, surface 30 31 Veronese, surface, moving frame of 291 Veronese, variety 30 31 34 37 41 62—72 87 131 132 Veronese, variety, 2-dimensional 67 285 290 291 295 Veronese, variety, 2nd fundamental form of 41 287 Veronese, variety, 2nd osculating subspace of 42 Veronese, variety, dimension of 38 Veronese, variety, tangent subspace to 38 Vertex of cone 116 119 120 126—128 135 168 170 Vertex of conic submanifold 168 Vertex of hypercone 122 131 Vieta theorem 204 276 Villa v 71 111 328 329 Vilms vii 330 Volume element 186 Vorontsova 207 300 330 Voss normal 111 Vygodsky 330 Wagner 268 330 Waksman 171 330 Walter 171 172 301 330 Web, multidimensional 276 296 Weise 199 206 331 Weise's scheme 206 207 Wilczynski v 330 Wilczynski directrix 250 Wilczynski — Bompiani quadric 249 Wood 275 276 295 330 Yanenko 141 330 Yang 330 331 Yano 296 320 Zaits 207 316 Zero direction 214 Zero matrix 116
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