球面中Ricci平行的超曲面

On Hyper-curved-surfaces in Sphere with Parallel Ricci Curvature

证明了球面中的Clifford极小超曲面是球面中唯一的Ricci平行的极小超曲面．并在一定条件下给出了球面中Ricci平行的超曲面的局部常曲率流形的乘积结构．

In the paper we prove that the Clifford minimal hyper-curved-surface of a sphere is the unique minimal hyper-curved-surface of a sphere with parallel Ricci curvature.We also set up a local product structure for the hyper-curved-surfaces in a sphere with the parallel Ricci curvature in which each factor has constant sectional curvature under a simple condition.