# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 38 (2009) pp.361-408

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### 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.

MSC(Primary) 53C40 53C42, 53C50 Lorentz surfaces, marginally trapped surfaces, Lagrangian surfaces, Lorentzian complex plane, surface of constant curvature.