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Classification of marginally trapped surfaces of constant curvature in Lorentzian complex plane. (English) Zbl 1187.53056
The author studies marginally trapped surfaces in the Lorentzian complex plane (i.e. surfaces with light-like mean curvature vector field). The main result classifies marginally trapped surfaces with constant curvature into twenty-one types. A rigidity theorem states that, locally, any marginally trapped surface with constant curvature in the Lorentzian complex plane is one of these twenty-one families, modulo a rigid motion and/or a dilation.

MSC:
53C40 Global submanifolds
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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