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Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.4 P.322~328


A rigidity theorem for submanifolds in Sn+p with constant scalar curvature

Author(s):  ZHANG Jian-feng

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310028, China; more

Corresponding email(s):   zjf7212@163.com

Key Words:  Scalar curvature, Mean curvature vector, The second fundamental form

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.

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author="ZHANG Jian-feng",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

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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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%D 2005
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2005.A0322

T1 - A rigidity theorem for submanifolds in Sn+p with constant scalar curvature
A1 - ZHANG Jian-feng
J0 - Journal of Zhejiang University Science A
VL - 6
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SP - 322
EP - 328
%@ 1673-565X
Y1 - 2005
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2005.A0322

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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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