On the theory of almost Grassmann structures
Differential Geometry
2007-05-23 v1
Abstract
The differential geometry of almost Grassmann structures defined on a differentiable manifold of dimension n = pq by a fibration of Segre cones SC (p, q) is studied. The peculiarities in the structure of almost Grassmann structures for the cases p=q=2; p = 2, q > 2 (or p > 2, q = 2), and p > 2, q > 2 are clarified. The fundamental geometric objects of these structures up to fourth order are derived. The conditions under which an almost Grassmann structure is locally flat or locally semiflat are found for all cases indicated above.
Cite
@article{arxiv.math/9805109,
title = {On the theory of almost Grassmann structures},
author = {Maks A. Akivis and Vladislav V. Goldberg},
journal= {arXiv preprint arXiv:math/9805109},
year = {2007}
}
Comments
LaTeX, 38 pages; to be published in Proceedings of the International Conference on Differential Geometry (Eotvos University, Budapest, 1996), Kluwer Academic Publishers, 1998