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Classification of pseudo-umbilical slant surfaces in Lorentzian complex space forms. (English) Zbl 1230.53052
Summary: We prove that slant surfaces in a non-flat Lorentzian complex space form must be Lagrangian. By applying this result, we completely classify pseudo-umbilical slant surfaces in Lorentzian complex space forms. Our classification results state that there exist two families of pseudo-umbilical slant surfaces in Lorentzian complex plane 1 2 , three families in complex projective plane P 1 2 and three families in complex hyperbolic plane H 1 2 .
53C40Global submanifolds (differential geometry)
53D12Lagrangian submanifolds; Maslov index
53C42Immersions (differential geometry)