deSitter空间S_1~(n+1)(c)中具有常平均曲率的n维完备类空超曲面

设M是de Sitter空间S1n+1(c)中具有常平均曲率的n维完备类空超曲面,文章证明了:当H2>c,n=2或者n2H2≥4(n-1)cn,≥3时,如果M的第二基本形式模长平方S<-nc+(n/2(n-1))n2H2-(n-2)∣H∣√n2H2-4(n-1)c],则M是全脐超曲面。

n-dimensional Complete Space-like Hypersurfaces with ConstantMean Curvature in a de Sitter Space S_1~(n+1)(c)

Let M be a n-dimensional complete space-like hyersurface with constant mean curvature in a de Sitter space S(c).In this paper,it is proved that when H2>c,n=2 or n2H2≥4(n-1)c,n≥3 if the square of lenth of the second fundamental form of M:S<-nc+(n/2(n-1))n2H2-(n-2)∣H∣√n2H2-4(n-1)c],then M is totally umbilical hypersurfaces.