拟常曲率空间的紧致极小子流形

Compact minimal submanifolds in Ricmannian manifold of quasi constant curvature

给出 QC 空间紧极小子流形全测地的截面曲率和数量曲率的 Pinching条件,推广了前人在常曲率空间的相应结果。即:k>(p—1)/((2p—1)或k>n/[2(n+1)]时 M=S_((1))~n;R>n(n—1)—n/[2—(1/p)]时,M=S_((1))~n.

The pinching conditions of sectional curvature and scalar curvature are given when a compact minimal submanifold in a Riemannian manifold of quasi constant curvature is a totally geodesic submanifold.A wide use is made of the Theorems put forward by formev researchers on the space as a constant curvature space form,i.e.if k>(p-1)/(2p -1)or k>[n/2(n+1)]then M=S^n(1);if R>n(n-1)-n/(2-1/p)then M=S^n(1).