| A rigidity theorem for submanifolds in S^n＋p with constant scalar curvature |
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| 引用本文： | 张剑锋.A rigidity theorem for submanifolds in S^n＋p with constant scalar curvature[J].浙江大学学报(A卷英文版),2005,6(4):322-328. |
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| 作者姓名： | 张剑锋 |
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| 作者单位： | DepartmentofMathematics,ZhejiangUniversity,Hangzhou310028,China／／DepartmentofMathematics,LishuiTeachers＇College,Lishui323000,China |
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| 摘 要： | Let M‘ be a closed submanifold isometrically immersed in a unit sphere S^n p. Denote by R, H and S, the normalized scalar curvature, the mean curvature, and the square of the length of the second fundamental form of M‘, respectively. Suppose R is constant and ≥1. We study the pinching problem on S and prove a rigidity theorem for M‘ immersed in S^n p with parallel normalized mean curvature vector field. When n≥8 or, n=7 and p≤2, the pinching constant is best.
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| 关 键 词： | 子簇 代数几何 弯曲率 刚性法则 |
| 收稿时间： | 6 June 2004 |
| 修稿时间： | 1 December 2004 |
A rigidity theorem for submanifolds inS
n+p with constant scalar curvature |
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| Zhang Jian-feng.A rigidity theorem for submanifolds inS
n+p with constant scalar curvature[J].Journal of Zhejiang University Science,2005,6(4):322-328. |
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| Authors: | Zhang Jian-feng |
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| Institution: | (1) Department of Mathematics, Zhejiang University, 310028 Hangzhou, China;(2) Department of Mathematics, Lishui Teachers’ College, 323000 Lishui, China |
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| Abstract: | LetM
1 be a closed submanifold isometrically immersed in a unit sphereS
n+p. Denote byR, H andS, the normalized scalar curvature, the mean curvature, and the square of the length of the second fundamental form ofM
1, respectively. SupposeR is constant and ≥1. We study the pinching problem onS and prove a rigidity theorem forM
1 immersed inS
n+p with parallel normalized mean curvature vector field. Whenn≥8 or,n=7 andp≤2, the pinching constant is best.
Project supported by the Stress Supporting Subject Foundation of Zhejiang Province, China |
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| Keywords: | Scalar curvature Mean curvature vector The second fundamental form |
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