Surfaces with parallel mean curvature in warped product spaces

In this work, we obtain a geometric description of surfaces $M^2$ of arbitrary codimension in the warped product $\mathbb{R}{\times }_{\rho }{\mathbb{Q}}_{\epsilon }^n$, with parallel mean curvature vector field in the normal connection, extending a result by Alencar-do Carmo-Tribuzy.