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A rigidity theorem for submanifolds in Sn+p with constant scalar curvature
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ZHANG Jian-feng. A rigidity theorem for submanifolds in Sn+p with constant scalar curvature[J]. Journal of Zhejiang University Science A, 2005, 6(4): 322-328.
@article{title="A rigidity theorem for submanifolds in Sn+p with constant scalar curvature",
author="ZHANG Jian-feng",
journal="Journal of Zhejiang University Science A",
volume="6",
number="4",
pages="322-328",
year="2005",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2005.A0322"
}
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%T A rigidity theorem for submanifolds in Sn+p with constant scalar curvature
%A ZHANG Jian-feng
%J Journal of Zhejiang University SCIENCE A
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%P 322-328
%@ 1673-565X
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%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2005.A0322
TY - JOUR
T1 - A rigidity theorem for submanifolds in Sn+p with constant scalar curvature
A1 - ZHANG Jian-feng
J0 - Journal of Zhejiang University Science A
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SP - 322
EP - 328
%@ 1673-565X
Y1 - 2005
PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2005.A0322
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.
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