本文得到高维球面上三维紧致极小子流形的若干刚性定理．在一个整体拚挤条件下，数量曲率的拚挤常数被改进了，也对李奇曲率的拚挤问题进行了讨论．

In this paper, we give some rigidity theorems which concern with 3-dim compact minimal submanifolds in a hight-dim sphere. Under a global pinching condition, the pinching constant on the scalar curvature is improved. We also study the problem of rigidity of Ricci curvature.