## Hypersurfaces in a sphere with constant mean curvature

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- by Zhong Hua Hou
- Proc. Amer. Math. Soc.
**125**(1997), 1193-1196 - DOI: https://doi.org/10.1090/S0002-9939-97-03668-X
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## Abstract:

Let $M^n$ be a closed hypersurface of constant mean curvature immersed in the unit sphere $S^{n+1}$. Denote by $S$ the square of the length of its second fundamental form. If $S<2\sqrt {n-1}$, $M$ is a small hypersphere in $S^{n+1}$. We also characterize all $M^n$ with $S=2\sqrt {n-1}$.## References

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## Bibliographic Information

**Zhong Hua Hou**- Affiliation: Department of Mathematics, Tokyo Institute of Technology, Japan; Department of Applied Mathematics, Dalian University of Technology, People’s Republic of China
- Email: hou@math.titech.ac.jp
- Received by editor(s): July 27, 1995
- Communicated by: Peter Li
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**125**(1997), 1193-1196 - MSC (1991): Primary 53C42, 53A10
- DOI: https://doi.org/10.1090/S0002-9939-97-03668-X
- MathSciNet review: 1363169