Maximal translation surfaces in Lorentz-Minkowski space

Source abstract

A translation surface in Lorentz-Minkowski space $\mathbb{L}^3$ is a surface defined as the sum of two spatial curves in $\mathbb{L}^3$. In this paper, we present a classification of maximal translation surfaces. We prove that if one of the generating curves is planar, then the other must also be planar. Moreover, we provide a complete description of these surfaces. When both planar curves are of Frenet type, we generalize the known examples of Scherk surfaces. In the case where one of the generating curves is a pseudo-null, we obtain examples of maximal surfaces. These surfaces do not have counterparts in Euclidean space.