On the theory of almost Grassmann structures

Details On the theory of almost Grassmann structures On the theory of almost Grassmann structures

1998-05-23

arxiv.org/abs/math/9805109v1

Proc. Conf. Dif. Geom. Budapest 1996, Kluwer 1999 1-37

Mathematics

Differential Geometry

LaTeX, 38 pages; to be published in Proceedings of the International Conference on Differential Geometry (Eotvos University, B

Scientific paper

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.

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