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

Márcio Batista; Marcos P. Cavalcante; Dorel Fetcu

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arXiv · 1402.1231

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

Márcio Batista·Marcos P. Cavalcante·Dorel Fetcu

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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.

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Márcio Batista, Marcos P. Cavalcante, Dorel Fetcu. 2014-02-06. Constant Mean Curvature Surfaces in $\mathbb{M}^2(c)\times\mathbb{R}$ and Finite Total Curvature. https://arxiv.org/abs/1402.1231

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