Mathematical Research Letters
Volume 24 (2017)
A characterization of Clifford hypersurfaces among embedded constant mean curvature hypersurfaces in a unit sphere
Pages: 503 – 534
Let $\Sigma$ be an $n(\geq 3)$-dimensional compact embedded hypersurface in a unit sphere with constant mean curvature $H \geq 0$ and with two distinct principal curvatures $\lambda$ and $\mu$ of multiplicity $n-1$ and $1$, respectively. It is known that if $\lambda \gt \mu$, there exist many compact embedded constant mean curvature hypersurfaces . In this paper, we prove that if $\mu \gt \lambda$, then $\Sigma$ is congruent to a Clifford hypersurface. The proof is based on the arguments used by Brendle .
Clifford hypersurface, Simons-type identity, constant mean curvature, embedded hypersurface
2010 Mathematics Subject Classification
Paper received on 8 June 2015.