华东交通大学学报2011，Vol.28Issue(2)：35-40,6.
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
摘要
Abstract
Let M be a complete space-like hypersurface with constant mean curvature H in a conformally flat Lorentzian manifold Ln+1 . Assume that the normal vectors of M be the main Ricci direction of Ln+ 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 ,then 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Key words
conformally flat/ Lorentzian manifold/ totally umbilical/ hypersurface分类
数理科学引用本文复制引用
吴泽九..共形平坦Lorentz流形中具常平均曲率的超曲面[J].华东交通大学学报,2011,28(2):35-40,6.基金项目
江西省教育厅青年科学基金项目(GJJ11044) （GJJ11044）
