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

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