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Trudy Geometricheskogo Seminara, 1973, Volume 4, Pages 167–178
(Mi intg42)
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Rigged hypercomplexes of quadratic elements
V. S. Malakhovskii
Abstract:
In $n$-dimensional projective space $n$-pararnetric family of $(n-2)$-dimensional non-degenerate quadrics (quadric elements) with given $(n-m-1)$-subspaces in their hyperplanes is considered.
In § 1 the differential equations of the hypercomplex $V_n$ of quadric elements and fields of different geometrical objects on $V_n$ are given.
In § 2 a distribution of $(n-m-1)$-subspaces in the hyperplanes of the hypercomplex $V_n$ is defined. Such a hypercomplex $V_n$ (hypercomplex $V_{n,m}$) is an $n$-dimensional manifold of pairs of figures $F_1$, $F_2$, where $F_1$ is a quadric element and $F_2$ — $(n-m-1)$-dimensional subspace of hyperplane of $F_1$.
In § § 3, 4 the constructions are carried out in a polarcanonized moving frame. Different objects intrinsically defined by the tangent distribution are studied.
Citation:
V. S. Malakhovskii, “Rigged hypercomplexes of quadratic elements”, Tr. Geom. Sem., 4, VINITI, Moscow, 1973, 167–178
Linking options:
https://www.mathnet.ru/eng/intg42 https://www.mathnet.ru/eng/intg/v4/p167
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