| An optimal rigidity theorem for complete submanifolds in a sphere |
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| 作者单位： | XU Hong-wei ZHU Jiao-feng Center of Math.Sci.，Zhejiang Univ.，Hangzhou 310027，China. |
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| 基金项目： | 国家自然科学基金，教育部跨世纪优秀人才培养计划 |
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| 摘 要： | It is proved that if M^n is an n-dimensional complete submanifold with parallel mean curvature vector and flat normal bundle in S^n＋p（1）, and if supM S 〈 α（n, H）, where α（n,H）=n＋n^3/2（n-1）H^2-n（n-2）/n（n-1）√n^2H^4＋4（n-1）H^2,then M^n must be the totally urnbilical sphere S^n（1/√1＋H^2）.An example to show that the pinching constant α（n, H） appears optimal is given.
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| 关 键 词： | 子流形 硬度 平均曲率 球面 |
| 收稿时间： | 9 June 2006 |
An optimal rigidity theorem for complete submanifolds in a sphere |
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| Authors: | Hong-wei Xu Jiao-feng Zhu |
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| Institution: | Center of Math. Sci., Zhejiang Univ., Hangzhou 310027, China |
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| Abstract: | It is proved that if Mn is an n-dimensional complete submanifold with parallel mean curvature vector and flat normal bundle in Sn p(1), and if SUPM S<α(n, H), where,α(n,H)=n n3/2(n-1)H2-n(n-2)/2(n-1)√n2H4 4(n-1)H2 ,then Mn must be the totally umbilical sphere Sn(1/√1 H2). An example to show that the pinching constantα (n, H) appears optimal is given. |
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| Keywords: | submanifold rigidity flat normal bundle mean curvature |
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