1998/05/23 by Maks A. Akivis, Vladislav V. Goldberg
Mathematics · #math.DG #msc:53C15 #msc:53C10
published as Proc. Conf. Dif. Geom. Budapest 1996, Kluwer 1999 1-37 · LaTeX, 38 pages; to be published in Proceedings of the International Conference on Differential Geometry (Eotvos University, Budapest, 1996), Kluwer Academic Publishers, 1998
arxiv created 1998/05/23 · arxiv updated 2009/11/30
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.