局部对称Lorentz流形中具常平均曲率的完备超曲面  

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

作　　者：吴泽九[1] 

机构地区：[1]华东交通大学基础科学学院,江西南昌330013

出　　处：《华东交通大学学报》2008年第1期97-101,共5页Journal of East China Jiaotong University

基　　金：华东交通大学科研基金资助(06ZKJC04)

摘　　要：设Ln1+1是截面曲率KL满足b/2<a≤KL≤b的局部对称Lorentz流形,M是Ln1+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Ln1+1的截面曲率K(ei∧en+1)满足∑iiλK(ei∧en+1)=nbH,则(i)S<2n-1(2a-b)时,M全脐;(ii)S=2n-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]中相应结果的推广与改进.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 reference[3]

关 键 词：局部对称 LORENTZ流形 类空超曲面 全脐 

分 类 号：O186[理学—数学]