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

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.

13 pages