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Grassmann geometries on compact symmetric spaces of general type

机译:一般型紧对称空间上的Grassmann几何

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This study is a continuation of my papers, Let M be a compact simply connected riemannian symmetric space of dimension m ( ≥ 2), and s an integer such that 1 ≤ s ≤ m. Let G~s(T_PM) be the set of s-dimensional linear subspaces in a tangent space T_pM and denote by G~S(TM) the Grassmann bundle over M with fibres G~S(T_PM). For an arbitrary subset V in G~S(TM) an s-dimensional connected sub-manifold S of M is called a V-submanifold if at each point p of S the tangent space T_PS belongs to V. The collection of V-submanifolds, denoted by g(M, V), constitutes a V-geometry. The term "Grassmann geometries" in the title is a collected name for such V-geometries and it has been introduced in R. Harvey-H. B. Lawson.
机译:这项研究是我论文的延续,设M为一个紧凑的简单连接的维为m(≥2)的s黎曼对称空间,s为1≤s≤m的整数。令G_s(T_PM)为切线空间T_pM中的s维线性子空间的集合,并由G〜STM表示M上具有纤维G〜S(T_PM)的格拉斯曼束。对于G〜STM中的任意子集V,如果在S的每个点p处切线空间T_PS属于V,则M的s维连接子流形S称为V-子流形。由g(M,V)表示的V构成V几何。标题中的“格拉斯曼几何”一词是此类V几何的统称,已在R. Harvey-H中引入。劳森。

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