| HYPERSURFACES IN SPACE FORMS WITH SCALAR CURVATURE CONDITIONS |
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| 作者姓名： | 徐森林 张运涛 |
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| 作者单位： | [1]DepartmentofMathematics,CentralChinaNormalUniversity,Wuhan430079,China [2]DepartmentofMathematics,UniversityofScienceandTechnologyofChina,Hefei230026,China |
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| 摘 要： | Let f : M^n→S^n 1真包含于R^n 2 be an n-dimensional complete oriented Riemannian manifold minimally immersed in an (n 1)-dimensional unit sphere S^n 1. Denote by S^n 1 the upper closed hemisphere. If f(M^n)包含于S ^n 1, then under some curvature conditions the authors can get that the isometric immersion is a totally embedding. They also generalize a theorem of Li Hai Zhong on hypersurface of space form with costant scalar curvature.
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| 关 键 词： | 超曲面 数量曲率 Riemannian流形 等距浸入 |
HYPERSURFACES IN SPACE FORMS WITH SCALAR CURVATURE CONDITIONS |
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| Xu Senlin.HYPERSURFACES IN SPACE FORMS WITH SCALAR CURVATURE CONDITIONS[J].Acta Mathematica Scientia,2004,24(1):39-44. |
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| Authors: | Xu Senlin |
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| Institution: | Xu Senlin Department of Mathematics,Central China Normal University,Wuhan 430079,China
Zhang Yuntao
Department of Mathematics,University of Science and Technology of China,Hefei 230026,China |
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| Abstract: | Let f: Mn → Sn 1(∩) Rn 2 be an n-dimensional complete oriented Riemannian manifold minimally immersed in an (n 1)-dimensional unit sphere Sn 1. Denote by Sn 1 the upper closed hemisphere. If f(Mn)(∩-) Sn 1 , then under some curvature conditions the authors can get that the isometric immersion is a totally embedding. They also generalize a theorem of Li Hai Zhong on hypersurface of space form with costant scalar curvature. |
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| Keywords: | Hypersurface scalar curvature space form |
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