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arXiv · 1305.2379

Simons' type equation for $f$-minimal hypersurfaces and applications

Xu Cheng·Tito Mejia·Detang Zhou
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Abstract

We derive the Simons' type equation for $f$-minimal hypersurfaces in weighted Riemannian manifolds and apply it to obtain a pinching theorem for closed $f$-minimal hypersurfaces immersed in the product manifold $\mathbb{S}^n(\sqrt{2(n-1)})\times \mathbb{R}$ with $f=\frac {t^2}{4}$. Also we classify closed $f$-minimal hypersurfaces with $L_f$-index one immersed in $\mathbb{S}^n(\sqrt{2(n-1)})\times \mathbb{R}$ with the same $f$ as above.

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Xu Cheng, Tito Mejia, Detang Zhou. 2013-05-10. Simons' type equation for $f$-minimal hypersurfaces and applications. https://arxiv.org/abs/1305.2379

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