Marginally trapped surfaces with pointwise 1-type Gauss map in Minkowski 4-space

A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. In the present paper we find all marginally trapped surfaces with pointwise 1-type Gauss map. We prove that a marginally trapped surface is of pointwise 1-type Gauss map if and only if it has parallel mean curvature vector field.