局部对称Lorentz流形中具常平均曲率的完备超曲面

设L1^n＋1是截面曲率KL满足b/2＜α≤KL≤b的局部对称Lorentz流形，M是L1^n＋1中具常平均曲率H的完备类空超曲面，S是M的第二基本形式模长平方，λ1，λ2……λn是M在点x处的n个主曲率，本文得到：如果L1^n＋1的截面曲率K（ei∧en＋1）满足∑λiK（ei∧en＋1）=nbH，则（i）S＜2√n-1（2a-b）时，M全脐：（ii）S=＜2√n-1（2a-b）时，若n=2，M全脐：若n≥3，M是双曲柱面。该结论是文3]中相庆结果的推广与改进。

Complete Space-like Hypersurfaces with Constant Mean Curvature in a Locally Symmetric Lorentzian Manifold

Let L1^n＋1be a locally symmetric Lorentzian manflold with sectional curature KL satisfying the condition2/b〈a≤KL≤b and M be an complete space-like hypersurface with constant mean curvature H in L1^n＋1,the square of the norm of the second fundamental form of M is denoted by S,λ1,λ2……λn are the principal curvatures at point x of M. Assume that the sectional curvature K（ei∧en＋1）of L1^n＋1 satisfys ∑λiK（ei∧en＋1）=nbH,（i）If S〈2√n-1（2a-b）,then M is totally umibilic;（ii）S=〈2√n-1（2a-b）,then M is totally umibilic when n = 2 and M is a hyperbolic cylinder when n≥3,, which generalizes and improves the corresponding results in reference3]