Author:

Abstract:

The Gaussian curvature of a surface has been studied extensively in the literature. Based on the second fundamental form of a surface, the second Gaussian curvature is introduced, opening up a whole new terrain of interest. With this paper we want to contribute to the exploration of this area. In particular, a characterization of translation surfaces with vanishing second Gaussian curvature in the 3-dimensional Euclidean and Minkowski space is obtained. In order to produce examples, non-linear second order ODE's need to be solved, which results in the introduction of the less familiar Lambert W function.