Semiintegrable almost Grassmann structures

Document Type

Article

Publication Date

1-1-1999

Abstract

In the present paper we study locally semiflat (we also call them semiintegrable) almost Grassmann structures. We establish necessary and sufficient conditions for an almost Grassmann structure to be α-or β-semiintegrable. These conditions are expressed in terms of the fundamental tensors of almost Grassmann structures. Since we are not able to prove the existence of locally semiflat almost Grassmann structures in the general case, we give many examples of α-and β-semiintegrable structures, mostly four-dimensional. For all examples we find systems of differential equations of the families of integral submanifolds Vα and Vβ of the distributions △α and △β of plane elements associated with an almost Grassmann structure. For some examples we were able to integrate these systems and find closed form equations of submanifolds Vα and Vβ.

Identifier

0033130319 (Scopus)

Publication Title

Differential Geometry and Its Application

External Full Text Location

https://doi.org/10.1016/S0926-2245(99)00014-5

ISSN

09262245

First Page

257

Last Page

294

Issue

3

Volume

10

This document is currently not available here.

Share

COinS