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Minimal flat Lorentzian surfaces in Lorentzian complex space forms. (English) Zbl 1199.53115
Summary: In this article we study minimal flat Lorentzian surfaces in Lorentzian complex space forms. First we prove that, for minimal flat Lorentzian surfaces in a Lorentzian complex form, the equation of Ricci is a consequence of the equations of Gauss and Codazzi. Then we classify minimal flat Lorentzian surfaces in the Lorentzian complex plane 1 2 . Finally, we classify minimal flat slant surfaces in Lorentzian complex projective plane ℂℙ 1 2 and in Lorentzian complex hyperbolic plane ℂℍ 1 2 .
MSC:
53C40Global submanifolds (differential geometry)
53C42Immersions (differential geometry)
53C50Lorentz manifolds, manifolds with indefinite metrics