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SCALAR CURVATURE OF HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A SPHERE

Published online by Cambridge University Press:  01 May 2009

QING-MING CHENG ,
YIJUN HE  and
HAIZHONG LI
QING-MING CHENG
Affiliation:
Department of Mathematics, Faculty of Sciences and Engineering, Saga University, Saga 840-8502, Japan e-mail: cheng@ms.saga-u.ac.jp
YIJUN HE*
Affiliation:
School of Mathematical Sciences, Shanxi University, Taiyuan 030006, P.R. China e-mail: heyijun@sxu.edu.cn
HAIZHONG LI
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P.R. China e-mail: hli@math.tsinghua.edu.cn
*
†Corresponding author, partially supported by Youth Science Foundation of Shanxi Province, China (2006021001).
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Abstract

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Let M be an n-dimensional closed hypersurface with constant mean curvature H satisfying |H| ≤ ϵ(n) in a unit sphere Sn+1, n ≤ 7, and S the square of the length of the second fundamental form of M. There exists a constant δ(n, H) > 0, which depends only on n and H, such that if S0 ≤ S ≤ S0 + δ(n, H), then S ≡ S0 and M is isometric to a Clifford hypersurface, where ϵ(n) is a sufficiently small constant depending on n and .

Keywords

Primary 53C42Secondary 53B25
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 2 , May 2009 , pp. 413 - 423
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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