德西特空间中常平均曲率类空超曲面的全测地性

Totally Geodesic Property of Space-like Hyper-surfaces with Constant Mean Curvature in de Sitter Space

设dSn+1是n+1维单位de Sitter空间,且M是dSn+1中紧致无边的类空超曲面.记S为M的第二基本形式模长平方,ΔS是S的拉普拉斯.利用关于ΔS的一个已知估计公式,证明了如果M的平均曲率H是常数,则必有H≡S≡0,即M必是全测地的.

Let dS n+1 be the n+1 -dimensional unit de Sitter and M be a compact space-like hyper-surface without boundary in dS n+1 . Denote by S the squared length of the second form for M and by Δ S the Laplacian for S. In this paper we applied a known estimation formula for Δ S to prove that if the mean curvature H of M is a constant,then H≡S≡0 ,that is M must be totally geodesic.Our result improves some relevant theorem in a previous paper.