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JOURNALS // Itogi Nauki i Tekhniki. Seriya "Problemy Geometrii. Trudy Geometricheskogo Seminara" // Archive

Tr. Geom. Sem., 1973 Volume 4, Pages 167–178 (Mi intg42)

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.



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