| 仅有2个不同主曲率的球面子流形 |
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| 引用本文： | 李亮.仅有2个不同主曲率的球面子流形[J].合肥工业大学学报(自然科学版),2009,32(5). |
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| 作者姓名： | 李亮 |
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| 作者单位： | 安徽交通职业技术学院,文理科学系,安徽,合肥,230051 |
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| 摘 要： | 文章给出了Cheng提出的一个公开问题的部分肯定的回答, 即证明了若单位球面的紧致超曲面M不仅具有常数量曲率n(n-2), 而且仅有2个不同主曲率, 其中一个是单重的, 则M等距于环面S1(√1/n)×Sn-1(√(n-1)/n);此外, 给出了Cheng的结果在紧致情形下的一个简单证明.
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| 关 键 词： | 主曲率 数量曲率 第2基本形式 等距 |
Submanifolds with two distinct principal curvatures in the unit sphere |
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| LI Liang.Submanifolds with two distinct principal curvatures in the unit sphere[J].Journal of Hefei University of Technology(Natural Science),2009,32(5). |
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| Authors: | LI Liang |
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| Institution: | Dept.of Liberal Arts and Science;Anhui Communications Vocational & Technical College;Hefei 230051;China |
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| Abstract: | This paper presents a partly affirmative solution to an open problem introduced by Cheng in considering compact submanifolds.Furthermore,the paper gives a simple method to discuss the submanifolds with a general constant scalar curvature,and obtains some results analogous to those of Cheng. |
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| Keywords: | principal curvature scalar curvature the second fundamental isometric |
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