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JOURNALS // Proceedings of the Yerevan State University, series Physical and Mathematical Sciences // Archive

Proceedings of the YSU, Physical and Mathematical Sciences, 2002 Issue 1, Pages 34–38 (Mi uzeru551)

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.

UDC: 514.75

Received: 18.01.2001
Accepted: 20.03.2002



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