Hokkaido Mathematical Journal

CHEN B.-Y.,

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

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
MSC(Secondary)53C42, 53C50
Uncontrolled KeywordsLorentz surfaces, marginally trapped surfaces, Lagrangian surfaces, Lorentzian complex plane, surface of constant curvature.