de Sitter空间S_1^(n+1)中的有限型球型旋转超曲面

SPHERICAL ROTATIONAL HYPERSURFACES OF FINITE TYPE IN S_1^(n+1)

研究En+21中deSitter空间Sn+11的坐标函数是其Laplacian的特征函数的球型旋转曲面Mn,得到Mn或为Sn+11的极小或极大超曲面,或者可与Sn-1(a)×H1(-a2-1)或Sn-1(a)×S11(1-a2)叠合。

Properties of the spherical rotation hypersurface M^n whose coordinate functions are proper functions of their Laplaces in S^(n+1)_1 are studied.Further,the following result is obtained:M^n is either a minimal or maximal hypersurface or congruent to S^(n-1)(a)×H^1(-a^2-1) or S^(n-1)(a)×S^1_1(1-a^2).