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

Márcio Batista, Marcos P. Cavalcante, Dorel Fetcu

Published 2014-02-06, updated 2016-06-21Version 3

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.