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arXiv · 1605.08853

A Simons' type formula for cmc surfaces in homogeneous $3$-manifolds

Ningwei Cui
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Abstract

In this paper, we give a Simons' type formula for the cmc surfaces in homogeneous $3$-manifolds $E(κ,τ)$, $τ\neq0$. As an application, we give a rigidity result in the case of $κ> 4τ^2$ for the cmc surfaces under a pinching assumption of the second fundamental form.

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Ningwei Cui. 2016-05-28. A Simons' type formula for cmc surfaces in homogeneous $3$-manifolds. https://arxiv.org/abs/1605.08853

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