Surfaces with parallel mean curvature in warped product spaces

TL;DR

This paper characterizes surfaces with parallel mean curvature vectors in warped product spaces, extending previous geometric results to higher codimensions.

Contribution

It provides a new geometric description of such surfaces in warped products, generalizing earlier work to arbitrary codimension.

Findings

Extended the classification of surfaces with parallel mean curvature vectors

Provided a geometric description in warped product spaces

Generalized previous results to higher codimension surfaces

Abstract

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