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

  • Bubyakin Igor V., bubyakiniv@mail.ru M. K. Ammosov North-Eastern Federal University Institute of mathematics and Informatics 48 Kulakovsky Street, Yakutsk 677891, Russia
Keywords: Grassmann manifold, complexes of multidimensional planes, Grassmann mapping, Segre manifold

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.

References

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How to Cite
Bubyakin, I. ( ) “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), pp. 3-12. doi: https://doi.org/10.25587/SVFU.2017.2.9242.
Section
Mathematics