Geometry of five-dimensional complexes of two-dimensional planes in projective space
type: Item
instance of: scholarly article
title: Geometry of five-dimensional complexes of two-dimensional planes in projective space
zbMATH Open document ID: 0736.53005
DOI: 10.1007/BF01085493
author: I. V. Bubyakin
publication date: 1992-06-26T00:00:00Z
review text: In the projective space \(P_ 5\) the Grassmann manifold \(G(2,5)\) of 2- planes \(L\) is studied. The Grassmann mapping \(\mu\) of \(G(2,5)\) to the nine-parametric manifold \(\Omega(2,5)\) in the projective space \(P_{19}\) is considered. Let \(\ell\) be the image of \(L\). The asymptotic cones of directions of the second and third orders of \(\Omega(2,5)\) in \(\ell\) are studied. The projectivizations of these cones are certain Segre manifolds. In \(P_ 5\) a five-parametric system \(K\) (the complex \(K\)) of 2-planes \(L\) is studied. Under the mapping \(\mu\) there corresponds a manifold \(V\subset\Omega(2,5)\) to \(K\). With help of the introduced Segre manifolds six characteristic directions in \(\ell\in V\) are defined. To the integral curves of these directions there correspond torses of \(K\). Special configurations of characteristic directions are considered and the corresponding special cases of \(K\) are studied. Existence theorems and geometric properties are found in these cases.
Mathematics Subject Classification ID: 53A20
Mathematics Subject Classification ID: 53A25
zbMATH DE Number: 22843
zbMATH Keywords: Grassmann manifold
zbMATH Keywords: Segre manifolds
zbMATH Keywords: characteristic directions
reviewed by: Josef Vala
MaRDI profile type: Publication
cites work: Q5827465
cites work: Q5771577
published in: Functional Analysis and Its Applications
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description: scientific article; zbMATH DE number 22843