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arXiv · 2001.10134

On the Chern conjecture for isoparametric hypersurfaces

Zizhou Tang·Wenjiao Yan
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Abstract

For a closed hypersurface $M^n\subset S^{n+1}(1)$ with constant mean curvature and constant non-negative scalar curvature, the present paper shows that if $\mathrm{tr}(\mathcal{A}^k)$ are constants for $k=3,\ldots, n-1$ for shape operator $\mathcal{A}$, then $M$ is isoparametric. The result generalizes the theorem of de Almeida and Brito \cite{dB90} for $n=3$ to any dimension $n$, strongly supporting Chern's conjecture.

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Zizhou Tang, Wenjiao Yan. 2020-01-28. On the Chern conjecture for isoparametric hypersurfaces. https://arxiv.org/abs/2001.10134

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