Classification of marginally trapped surfaces of constant curvature in Lorentzian complex plane

Abstract

A surface in the Lorentzian complex plane ${\bf C}^2_1$ is called {\it marginally trapped\/} if its mean curvature vector is light-like at each point on the surface. In this article, we classify marginally trapped surfaces of constant curvature in the Lorentzian complex plane ${\bf C}^2_1$. Our main results state that there exist twenty-one families of marginally trapped surfaces of constant curvature in ${\bf C}^2_1$. Conversely, up to rigid motions and dilations, marginally trapped surfaces of constant curvature in ${\bf C}^2_1$ are locally obtained from these twenty-one families.