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

Let M~n be an n-dimensiooal 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 Mn 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.