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Proceedings of the Yerevan State University, series Physical and Mathematical Sciences, 2002, Issue 1, Pages 34–38
(Mi uzeru551)
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Mathematics
Possible complexes of three-dimensional planes in projective space $\mathbf{P}^6$ II
V. Nersesyan Yerevan State University, Faculty of Mathematics and Mechanics
Abstract:
In the work possible complexes of three-dimensional planes in six-measured projective space $\mathbf{P}^6$ are studied. It's proved that one-parametric family of cones of second order with three-dimensional flats forming and univariate top, which describes unfold surface defines four-parametric possible family of planes $E^3$, which are all three-dimensional forming to this cones.
It's also proved that if we take in space $\mathbf{P}^6$ four-parametric family of three-dimensional planes including fixed straight line $l$ and touching two hypercone with one general univariate top $l$ we will get possible family of three-dimensional planes. Corresponding family tangent of four-parametric family is formed by intersection of tangent hyperplanes to the cones in the sport of osculation of three- dimensional planes family with them.
Keywords:
Six-measured projective space, family of cones of second order with three-dimensional flats forming.
Received: 18.01.2001 Accepted: 20.03.2002
Citation:
V. Nersesyan, “Possible complexes of three-dimensional planes in projective space $\mathbf{P}^6$ II”, Proceedings of the YSU, Physical and Mathematical Sciences, 2002, no. 1, 34–38
Linking options:
https://www.mathnet.ru/eng/uzeru551 https://www.mathnet.ru/eng/uzeru/y2002/i1/p34
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