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Classification of marginally trapped Lagrangian surfaces in Lorentzian complex space forms. (English) Zbl 1121.53047
Summary: 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 C 1 2 , nine families in CP 1 2 , and nine families in CH 1 2 . Conversely, all marginally trapped Lagrangian surfaces in Lorentzian complex space forms are obtained from these 21 families.
MSC:
53C50Lorentz manifolds, manifolds with indefinite metrics
53D12Lagrangian submanifolds; Maslov index