Weierstrass-type representations for timelike surfaces

Abstract

In this paper we give the Weierstrass-type representation for Lorentz conformal minimal surfaces in Minkowski 3-space that was derived by Konderak, and a new one for Lorentz conformal constant mean curvature 1 surfaces in anti de Sitter 3-space, using integrable systems techniques. As an application, we analyze their singularities. Finally, we describe first steps toward discretization of these timelike surfaces.