Solitons of the mean curvature flow in S2 × R

Abstract

A soliton of the mean curvature flow in the product space S2 ×R is 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 of S2 × R. In this paper we consider the cases that X is the vector field tangent to the second factor and the vector field associated to 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 rotations of S2.