共形平坦Lorentz空间具常平均曲率的一类超曲面

设肘是共形平坦Lorentz空间L1^n＋1中具常平均曲率的完备类空超曲面，R与r分别表示L1^n＋1的Ricci曲率的上、下确界，C=2nr-（n＋1）R]／n（n-1）]。如果M的法向量是L1^n＋1的Ricci主方向，则（1）当M第二基本形式模长平方S〈2√n-1C时，肘全脐；（2）当S=2√n-1C时，若n=2，M是全脐超曲面；若n≥3，M是双曲柱面。

Some Hypersurfaces in a Conformally Flat Lorentzian Manifold with Constant Mean Curvature

Let M be a complete hypersurface with constant mean curvature in a n+1-dimensional conformally flat Lorentzian manifold Ln+11.Let S stands for the square of the length of the second fundamental form of M and C=2nr-(n+1)R]/n(n-1)],where R and r is the supremum and infimum of Ricci curvature of M respectively.Assume that the normal direction of M be the Ricci principal direction of Ln+11.(1) If S<2n-1C,then M is a totally umbilical hypersurface;(2) If S=2n-1C,then M is a totally umbilical hypersurface when ...