关于殆Grassmann结构理论
On the theory of almost Grassmann structures
摘要：
研究了由Segre锥SC（p，q）纤维化定义在n = pq的微分流形上的几乎Grassmann结构的微分几何.阐明了p=q=2，p = 2，q > 2（或p > 2，q = 2）和p > 2，q > 2的几乎Grassmann结构的结构特征.这些结构的基本几何对象的四阶推导。对于上述所有情形，我们都找到了几乎格拉斯曼结构是局部平坦或局部半平坦的条件。
英文摘要：
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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