NONLINEAR KLEIN-GORDON EQUATIONS AND LORENTZIAN MINIMAL SURFACES IN LORENTZIAN COMPLEX SPACE FORMS

摘要

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 C-1(2). Finally, we classify minimal slant surfaces in the Lorentzian complex projective plane CP12(4) and in the Lorentzian complex hyperbolic plane CH12(-4). In particular, our latter results show that if a minimal slant surface in CP12(4) or in CH12(-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.