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

Ningwei Cui

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

Differential Geometry 2016-05-31 v1

Authors: Ningwei Cui

Abstract

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

Cite

@article{arxiv.1605.08853,
  title  = {A Simons' type formula for cmc surfaces in homogeneous $3$-manifolds},
  author = {Ningwei Cui},
  journal= {arXiv preprint arXiv:1605.08853},
  year   = {2016}
}

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9 pages

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