共形和格拉斯曼结构
Conformal and Grassmann structures
摘要：
给出了共形结构和几乎格拉斯曼结构理论的主要结果。概述了这些结构的共同性质以及它们之间的差异。特别地，找到了这些结构的结构群及其微分代数，确定了几乎Grassmann结构的一个完全定义其几何结构的几何对象的完备系统。这些对象的消失决定了局部格拉斯曼流形。证明了可积的几乎Grassmann结构是局部Grassmann结构。证明了几乎Grassmann结构的半可积性准则的不变形式。
英文摘要：
The main results on the theory of conformal and almost Grassmann structures are presented. The common properties of these structures and also the differences between them are outlined. In particular, the structure groups of these structures and their differential prolongations are found. A complete system of geometric objects of the almost Grassmann structure totally defining its geometric structure is determined. The vanishing of these objects determines a locally Grassmann manifold. It is proved that the integrable almost Grassmann structures are locally Grassmann. The criteria of semiintegrability of almost Grassmann structures is proved in invariant form.
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