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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:

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53D12 Lagrangian submanifolds; Maslov index
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References:

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