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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 $\Bbb C^2_1$. Finally, we classify minimal flat slant surfaces in Lorentzian complex projective plane $\Bbb{CP}^2_1$ and in Lorentzian complex hyperbolic plane $\Bbb{CH}^2_1$.

53C40Global submanifolds (differential geometry)
53C42Immersions (differential geometry)
53C50Lorentz manifolds, manifolds with indefinite metrics
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