  A marginally trapped surface in the four-dimensional Minkowski space is a
spacelike surface whose mean curvature vector is lightlike at each point. We
introduce meridian surfaces of parabolic type as one-parameter systems of
meridians of a rotational hypersurface with lightlike axis in Minkowski 4-space
and find their basic invariants. We find all marginally trapped meridian
surfaces of parabolic type and give a geometric construction of these surfaces.
