| 正曲率子流形的几何刚性定理 |
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| 引用本文： | Xu Hongwei Han Wei. 正曲率子流形的几何刚性定理[J]. 高校应用数学学报(英文版), 2005, 20(4): 475-482. DOI: 10.1007/s11766-005-0027-3 |
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| 作者姓名： | Xu Hongwei Han Wei |
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| 作者单位： | Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027,China. |
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| 基金项目： | Supported by the National Natural Science Founation of China（10231010）;Trans-Century Training. Programme Foundation for Talents by the Ministry of Education of China and the Natural Science Foundation of Zhejiang Province（101037）. |
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| 摘 要： | §1Introduction LetMnbeann-dimensionalcompactRiemannianmanifoldisometricallyimmersedinto an(n+p)-dimentionalcompleteandsimplyconnectedRiemannianmanifoldFn+p(c)with constantcurvaturec.DenotebyKMandHthesectionalcurvatureandmeancurvatureofM respectively.In[10],Yauprovedthefollowingstrikingresult.TheoremA.LetMnbeann-dimensionalorientedcompactminimalsubmanifoldin Sn+p(1).IfthesectionalcurvatureofMisnotlessthanp-12p-1,thenMiseitherthetotally geodesicsphere,thestandardimmersionoftheproductoftw…
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| 关 键 词： | 几何刚性 子流形 平均曲率 组合曲率 黎曼流形 |
| 收稿时间： | 2005-03-14 |
Geometric rigidity theorem for submanifolds with positive curvature |
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| Xu Hongwei,Han Wei. Geometric rigidity theorem for submanifolds with positive curvature[J]. Applied Mathematics A Journal of Chinese Universities, 2005, 20(4): 475-482. DOI: 10.1007/s11766-005-0027-3 |
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| Authors: | Xu Hongwei Han Wei |
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| Affiliation: | Center of Mathematical Sciences,Zhejiang University,Hangzhou 310027,China;Center of Mathematical Sciences,Zhejiang University,Hangzhou 310027,China |
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| Abstract: | A geometric rigidity theorem for submanifolds with parallel mean curvature and positive curvature in a space form is proved. It is a generalization of the famous rigidity theorems due to S. T. Yau and others. |
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| Keywords: | submanifolds geometric rigidity mean curvature sectional curvature. |
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