A characterization of the Clifford torus

Cheng, Qing-Ming; Ishikawa, Susumu

doi:10.1090/S0002-9939-99-05088-1

A characterization of the Clifford torus
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by Qing-Ming Cheng and Susumu Ishikawa

Proc. Amer. Math. Soc. 127 (1999), 819-828

DOI: https://doi.org/10.1090/S0002-9939-99-05088-1

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Abstract:

In this paper, we prove that an $n$-dimensional closed minimal hypersurface $M$ with Ricci curvature $Ric(M) \geq \dfrac {n}{2}$ of a unit sphere $S^{n+1}(1)$ is isometric to a Clifford torus if $n\leq S\leq n+\frac {14(n+4)}{9n+30}$, where $S$ is the squared norm of the second fundamental form of $M$.

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