Constant Mean Curvature Surfaces in $\mathbb{M}^2(c)\times\mathbb{R}$ and Finite Total Curvature

Márcio Batista; Marcos P. Cavalcante; Dorel Fetcu

Constant Mean Curvature Surfaces in $\mathbb{M}^2(c)\times\mathbb{R}$ and Finite Total Curvature

Differential Geometry 2016-06-22 v3

Authors: Márcio Batista , Marcos P. Cavalcante , Dorel Fetcu

Abstract

We consider surfaces with parallel mean curvature vector field and finite total curvature in product spaces of type $\mathbb{M}^n(c)\times\mathbb{R}$ , where $\mathbb{M}^n(c)$ is a space form, and characterize certain of these surfaces. When $n=2$ , our results are similar to those obtained in \cite{bds} for surfaces with constant mean curvature in space forms.

Keywords

constant mean curvature surfaces parallel mean curvature vector field finite total curvature product spaces space form

Cite

@article{arxiv.1402.1231,
  title  = {Constant Mean Curvature Surfaces in $\mathbb{M}^2(c)\times\mathbb{R}$ and Finite Total Curvature},
  author = {Márcio Batista and Marcos P. Cavalcante and Dorel Fetcu},
  journal= {arXiv preprint arXiv:1402.1231},
  year   = {2016}
}

Comments

Updated version taking into account the remarks of the referee

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