Abstract
A Lagrangian surface in a Lorentzian Kähler surface is called marginally trapped if its mean curvature vector is lightlike at each point. In this paper we classify marginally trapped Lagrangian surfaces in Lorentzian complex space forms. Our main results state that there exist three families of marginally trapped Lagrangian surfaces in C12, nine families in CP12, and nine families in CH12. Conversely, all marginally trapped Lagrangian surfaces in Lorentzian complex space forms are obtained from these 21 families.
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