Surfaces with parallel mean curvature in $\mathbb{S}^3\times\mathbb{R}$ and $\mathbb{H}^3\times\mathbb{R}$

Dorel Fetcu; Harold Rosenberg

Surfaces with parallel mean curvature in $\mathbb{S}^3\times\mathbb{R}$ and $\mathbb{H}^3\times\mathbb{R}$

Differential Geometry 2011-04-01 v1

Authors: Dorel Fetcu , Harold Rosenberg

Abstract

We prove a Simons type equation for non-minimal surfaces with parallel mean curvature vector (pmc surfaces) in $M^3(c)\times\mathbb{R}$ , where $M^3(c)$ is a 3-dimensional space form. Then, we use this equation in order to characterize certain complete non-minimal pmc surfaces.

Keywords

parallel mean curvature simons type equation non-minimal surfaces space forms product manifolds

Cite

@article{arxiv.1103.6254,
  title  = {Surfaces with parallel mean curvature in $\mathbb{S}^3\times\mathbb{R}$ and $\mathbb{H}^3\times\mathbb{R}$},
  author = {Dorel Fetcu and Harold Rosenberg},
  journal= {arXiv preprint arXiv:1103.6254},
  year   = {2011}
}

Comments

13 pages

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