Proceedings of the American Mathematical Society

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Hypersurfaces in a sphere with constant mean curvature

Author(s): Zhong Hua Hou
Journal: Proc. Amer. Math. Soc. 125 (1997), 1193-1196.
MSC (1991): Primary 53C42, 53A10
MathSciNet review: 1363169
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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 $S=2\sqrt {n-1}$ .

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