Journal of Zhejiang University-SCIENCE A

, Volume 6, Issue 4, pp 322–328 | Cite as

A rigidity theorem for submanifolds inSn+p with constant scalar curvature

  • Zhang Jian-feng
Applied Mathematics and Engineering Management Science


LetM1 be a closed submanifold isometrically immersed in a unit sphereSn+p. Denote byR, H andS, the normalized scalar curvature, the mean curvature, and the square of the length of the second fundamental form ofM1, respectively. SupposeR is constant and ≥1. We study the pinching problem onS and prove a rigidity theorem forM1 immersed inSn+p with parallel normalized mean curvature vector field. Whenn≥8 or,n=7 andp≤2, the pinching constant is best.

Key words

Scalar curvature Mean curvature vector The second fundamental form 

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Copyright information

© Zhejiang University Press 2005

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang UniversityHangzhouChina
  2. 2.Department of MathematicsLishui Teachers’ CollegeLishuiChina

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