Screw invariant marginally trapped surfaces in Minkowski 4-space

Abstract

A spacelike surface in a Lorentzian manifold whose mean curvature vector is lightlike everywhere is called marginally trapped. The classification of marginally trapped surfaces in Minkowski 4-space which are invariant under a subgroup of the Lorentz group that leaves invariant a lightlike direction, i.e. the so-called screw invariant surfaces, is obtained. As corollaries, the screw invariant marginally trapped surfaces with harmonic mean curvature vector and with prescribed Gaussian curvature are explicitly described.