单位球面的超曲面的一个内蕴刚性定理

A INTRINSIC RIGIDITY THEOREM OF HYPERSURFACES IN S^(n+1)

设M是单位球面Sn+1无脐点超曲面,在Sn+1Moebius变换群下M的基本不变量是Moebius度量g,Moebius形式Φ,Moebius第二基本形式B和Blaschke张量A。本文我们证明如下主要定理:设x:M→Sn+1是Sn+1的无脐点超曲面,n3,Q和K分别是M关于Moebius度量的Ricci曲率的下确界和正规数量曲率,如果Moebius形式Φ平行,Q-K(nn-2)2,那么n为偶数且x:M→Sn+1Moebius等价于Clifford极小环x~:S2n(12)×S2n(12)→Sn+1。

This paper,proves the following main theorem:Let x:M→S n+1 be a hypersurface in S n+1 without umbilic point,n3,Q and K are respectively the infimum of Ricci curvature and normalized scalar curvature with respect to the Moebius Metric,if the Moebius form Φ is parallel and Q-K(n-2n) 2,then n is even and x is Moebius equavalent to the Clifford minimal torus :S n2 (12)×S n2 (12)→S n+1 .