球空间S^(n+p)(c)中的紧致极小子流形

The Compact Minimal Submanifold in Sphere S^(n+p)(c)

设Mn是常曲率空间S^(n+p)(c)中的紧致极小子流形,K和Q分别是M^n上每点各方向截面曲率和Ricci曲率的下确界,R是M^n的数量曲率.利用M^n的内在量Q,R和σ,给出球空间S^(n+p)(c)中的紧致极小子流形是全测地子流形的几个充分条件.

Let M^n be an n- dimensional compact minimal sub- manifold in S^（n＋p）（c） with constant curvature c. , let K and Q be the infimum of the sectional curvature and Ricci curvature of M^n respectively and let R be the scalar curvature of M^n and σ be the square of the length of the second fundamental form of M^n. The author obtains in this paper several sufficient conditions of M^n , which are the totally geodesic submanifold.