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

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

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。

Let M be a n-dimensional complete space-like hyersurface with constant mean curvature in a de Sitter space S16n＋1（c）.In this paper, it is proved that when H2〉c,n=2 or n^2H^2≥4（n-1）c,n≥3 if the square of lenth of the second fundamental form of M：S〈-nc＋n/2（n-1）[n^2H^2-（n-2）｜H｜√n^2H^2-4（n-1）c],then M is totally umbilical hypersurfaces.