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 Mathematical notes of NEFU, 2017, Volume 24, Issue 2, Pages 3–12 (Mi svfu177)

Mathematics

About the structure of five-dimensional complexes of two-dimensional planes in projective space $P^5$ with a single developable surface

I. V. Bubyakin

M. K. Ammosov North-Eastern Federal University, Institute of mathematics and Informatics, 48 Kulakovsky Street, Yakutsk 677891, Russia

Abstract: This article focuses on projective differential geometry of submanifolds of $2$-dimensional planes manifolds $G(2, 5)$ in projective space $P^5$ containing single developable surface. To study such submanifolds we use the Grassmann mapping of manifold $G(2, 5)$ of $2$-dimensional planes in projective space $P^5$ to $9$-dimensional algebraic manifold $\Omega (2, 5)$ of space $P^19$. This mapping combined with the method of external Cartan's forms and moving frame method made possible to determine the structure of considered manifolds.

Keywords: Grassmann manifold, complexes of multidimensional planes, Grassmann mapping, Segre manifold.

DOI: https://doi.org/10.25587/SVFU.2017.2.9242

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UDC: 514.755

Citation: I. V. Bubyakin, “About the structure of five-dimensional complexes of two-dimensional planes in projective space $P^5$ with a single developable surface”, Mathematical notes of NEFU, 24:2 (2017), 3–12

Citation in format AMSBIB
\Bibitem{Bub17} \by I.~V.~Bubyakin \paper About the structure of five-dimensional complexes of two-dimensional planes in projective space $P^5$ with a single developable surface \jour Mathematical notes of NEFU \yr 2017 \vol 24 \issue 2 \pages 3--12 \mathnet{http://mi.mathnet.ru/svfu177} \crossref{https://doi.org/10.25587/SVFU.2017.2.9242} \elib{http://elibrary.ru/item.asp?id=32371882}