| 共形平坦Lorentz流形中具常平均曲率的超曲面 |
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| 引用本文： | 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. |
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| 作者姓名： | 吴泽九 |
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| 作者单位： | 华东交通大学基础科学学院,江西,南昌,330013 |
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| 基金项目： | 江西省教育厅青年科学基金项目 |
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| 摘 要： | 设M是共形平坦Lorentz流形Ln1+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Ln1+1的Ricci主方向,C是与Ln1+1的Ricci曲率的上、下确界有关的常教,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...
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| 关 键 词： | 共形平坦 Lorentz流形 类空超曲面 全脐 |
Hypersurfaces with Constant Mean Curvature in a Conformally Flat Lorentzian Manifold |
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| Wu Zejiu.Hypersurfaces with Constant Mean Curvature in a Conformally Flat Lorentzian Manifold[J].Journal of East China Jiaotong University,2011,28(2):35-40. |
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| Authors: | Wu Zejiu |
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| Institution: | Wu Zejiu(School of Basic Sciences,East China Jiaotong University,Nanchang 330013,China) |
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| Abstract: | 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. |
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| Keywords: | conformally flat Lorentzian manifoldt otally umbilical hypersurface |
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