De Sitter空间中半对称的类空超曲面

Semi-symmetric spacelike hypersurfaces in De Sitter space

给出了 De Sitter空间 Sn+ 1 1 (1) (n≥ 3)的类空超曲面是半对称的充要条件 ,决定了 Sn+ 1 1 (1) (n≥ 3)的半对称类空超曲面的局部结构 ,证明了 Sn+ 1 1 (1) (n≥ 3)具有常平均曲率的连通完备的半对称类空超曲面或是全脐的 ,或是具有两个不同主曲率的等参超曲面 .

In this paper,the sufficient and necessary condition of a spacelike hypersurface in Sn+1_1(1)(n≥3) to be a semi-symmetric hyp ersurface is given,the local structure of a semi-symmetric spacelike hypersurfa ce in Sn+1_1(1)(n≥3) is determined,and the main theorem that a semi -symmetric spacelike hypersurface in Sn+1_1(1)(n≥3) with constant m ean curvature is either a totally umbilical hypersurface or a isoparametric hype rsurface with two distinct principal curvature is proved.