Solitons of the mean curvature flow in s²

A soliton of the mean curvature flow in the product space s² as a surface whose mean curvature H satisfies the equation H= N, X, where N is the unit normal of the surface and X is a Killing vector field. In this paper we consider the vector field tangent to the fibers and the vector field associated to a rotations about an axis of s², respectively. We give a classification of the solitons with respect to these vector fields assuming that the surface is invariant under a one-parameter group of vertical translations or under a group of rotations of s².