A Simons type formula for surfaces with parallel mean curvature

Dorel Fetcu; Harold Rosenberg

A Simons type formula for surfaces with parallel mean curvature

Differential Geometry 2011-02-03 v2

Authors: Dorel Fetcu , Harold Rosenberg

Abstract

We prove a Simons type equation for non-minimal surfaces with parallel mean curvature vector (pmc surfaces) in $M^n(c)\times\mathbb{R}$ , where $M^n(c)$ is an $n$ -dimensional space form. Then, we use this equation in order to characterize complete non-minimal pmc surfaces with non-negative Gaussian curvature.

Keywords

surfaces with constant mean curvature minimal surfaces hypersurfaces

Cite

@article{arxiv.1102.0219,
  title  = {A Simons type formula for surfaces with parallel mean curvature},
  author = {Dorel Fetcu and Harold Rosenberg},
  journal= {arXiv preprint arXiv:1102.0219},
  year   = {2011}
}

Comments

This paper has been withdrawn by the authors because equation 3.13 (the Simons type equation) is a particular case of formula 2.8 in [S.-Y. Cheng and S.-T. Yau, Hypersurfaces with constant scalar curvature, Math. Ann. 225(1977), 195--204

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