NONEXPANSIVE RETRACTIONS ONTO CLOSED CONVEX CONES IN BANACH SPACES

Abstract

We investigate Lorentzian minimal surfaces in Lorentzian complex space forms. First, we prove that for such surfaces the equation of Ricci is a consequence of the equations of Gauss and Codazzi. Next, we classify Lorentzian minimal surfaces in the Lorentzian complex plane ${\bf C}^2_1$. Finally, we classify minimal slant surfaces in the Lorentzian complex projective plane $CP^2_1(4)$ and in the Lorentzian complex hyperbolic plane $CH^2_1(-4)$. In particular, our latter results show that if a minimal slant surface in $CP^2_1(4)$ or in $CH^2_1(-4)$ contains no open subset of constant curvature, then it is of Klein-Gordon type which arises from the solutions of certain nonlinear Klein-Gordon equations.