Translators of the Mean Curvature Flow in the Special Linear Group SL(2, R)

Abstract

Translators in the special linear group are surfaces whose mean curvature H and unit normal vector N satisfy , where X is a fixed Killing vector field. In this paper we study and classify those translators that are invariant by a one-parameter group of isometries. By the Iwasawa decomposition, there are three types of such groups. The dimension of the Killing vector fields is 4 and an exhaustive discussion is done for each one of the Killing vector fields and each of the invariant surfaces. In some cases, explicit parametrizations of translators are obtained.