Graph Translation Surface in the Lorentz-Heisenberg 3-space with constant curvatures

Abstract

In this paper, we study graph translation surfaces in a 3-dimensional Lorentz-Heisenberg 3-space H3. The classification theorems of the considered surfaces with zero and nonzero mean and Gaussian curvatures are given. Contrary to the Euclidean case, there is evidence that , translation surfaces with constant Gaussian curvature K that are not cylindrical surfaces, with constant mean curvature H ̸= 0 which are not settled.