Minimal flat Lorentzian surfaces in Lorentzian complex space forms

Abstract

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