Null-translation surfaces with constant curvatures in Lorentz-Minkowski 3-space

Translation surface is a surface formed by two curves moving along each other. In this paper we analyze this kind of surfaces in Lorentz-Minkowski 3-space R13, which is the smooth manifold R3 endowed by a flat Lorentzian pseudometric. Translation surfaces in R13 can be classified with respect to the causal character of their generating curves (spacelike, timelike or null (lightlike)). We are specially interested in translation surfaces generated by at least one null curve, which we refer to as null-translation surfaces. In the present paper we determine all nulltranslation surfaces of constant mean curvature and prove that the only null-translation surfaces of constant Gaussian curvature are cylindrical surfaces