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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2005, Vol. 6 Issue (4): 322-328    DOI: 10.1631/jzus.2005.A0322
Applied Mathematics and Engineering Management Science     
A rigidity theorem for submanifolds in Sn+p with constant scalar curvature
ZHANG Jian-feng
Department of Mathematics, Zhejiang University, Hangzhou 310028, China; Department of Mathematics, Lishui Teachers’ College, Lishui 323000, China
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Abstract  Let Mn be a closed submanifold isometrically immersed in a unit sphere Sn+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 Mn, respectively. Suppose R is constant and ≥1. We study the pinching problem on S and prove a rigidity theorem for Mn immersed in Sn+p with parallel normalized mean curvature vector field. When n≥8 or, n=7 and p≤2, the pinching constant is best.

Key words： Scalar curvature      Mean curvature vector      The second fundamental form     
Received: 06 June 2004     
CLC:  O186  
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ZHANG Jian-feng. A rigidity theorem for submanifolds in Sn+p with constant scalar curvature. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6(4): 322-328.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2005.A0322     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2005/V6/I4/322

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