| 伪黎曼空间型中具有常数量曲率的类空子流形 |
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| 引用本文： | 文海燕,刘建成. 伪黎曼空间型中具有常数量曲率的类空子流形[J]. 山东大学学报(理学版), 2017, 52(10): 89-96. DOI: 10.6040/j.issn.1671-9352.0.2017.021 |
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| 作者姓名： | 文海燕 刘建成 |
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| 作者单位： | 西北师范大学数学与统计学院, 甘肃 兰州 730070 |
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| 基金项目： | 国家自然科学基金资助项目(11261051) |
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| 摘 要： | 设M n是伪黎曼空间型N n+pq(c)(1≤q≤p)中具有常数量曲率R的n维完备类空子流形。 假定M n在N n+pq(c)中的第二基本形式是局部类时的情况下, 应用Simons型不等式以及Cheng-Yau引进的二阶微分算子, 得到了M n的一个刚性结果。
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| 关 键 词： | 伪黎曼空间型 类空子流形 第二基本形式 常数量曲率 |
| 收稿时间： | 2017-01-23 |
Space-like submanifolds with constant scalar curvature in the pseudo-Riemannian space forms |
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| WEN Hai-yan,LIU Jian-cheng. Space-like submanifolds with constant scalar curvature in the pseudo-Riemannian space forms[J]. Journal of Shandong University, 2017, 52(10): 89-96. DOI: 10.6040/j.issn.1671-9352.0.2017.021 |
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| Authors: | WEN Hai-yan LIU Jian-cheng |
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| Affiliation: | College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China |
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| Abstract: | Let M n be a space-like submanifold immersed in a pseudo-Riemannian space form N n+pq(c) with constant scalar curvature. Assume the second fundamental form of M n in N n+pq(c) is locally time-like, by applying Simons inequality and Cheng-Yau modified operator, a rigidity theorem of M n is obtained. |
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| Keywords: | pseudo-Riemannian space form space-like submanifold constant scalar curvature the second fundamental form |
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