共形平坦Lorentz流形中具常平均曲率的超曲面  

Hypersurfaces with Constant Mean Curvature in a Conformally Flat 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》2011年第2期35-40,共6页Journal of East China Jiaotong University

基　　金：江西省教育厅青年科学基金项目(GJJ11044)

摘　　要：设M是共形平坦Lorentz流形L1n+1中具常平均曲率H的完备类空超曲面。如果M的法向量是L1n+1的Ricci主方向,C是与L1n+1的Ricci曲率的上、下确界有关的常数,则(1)当H2≤C,n=2或n2H2<4(n-1)C,n≥3时,M全脐;(2)当n2H2=4(n-1)C,n≥3时,M是全脐球面Sn或是双曲柱面H1(r)′Sn-1(t)。此结论推广与改进了文[2]与[3]中的结果。Let M be a complete space-like hypersurface with constant mean curvature H in a conformally flat Lorentzian manifold L1n＋1.Assume that the normal vectors of M be the main Ricci direction of L1n＋1 and C be a constant related to the supremum and infimum of Ricci curvature of M.（1）If H2 ≤C when n=2 or n2H2 4（n-1）C when n≥3 t,hen M is a totally umibilic hypersurface;（2）If n2H2 = 4（n-1）C when n≥3,then M is a totally umibilic sphere or a hyperbolic cylinder H1（r）′Sn-1（t）.The corresponding results in [2] and [3] are generalized.

关 键 词：共形平坦 LORENTZ流形 类空超曲面 全脐 

分 类 号：O186.12[理学—数学]