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

Year 2022, Volume: 19 Issue: 1, 13 - 21, 01.05.2022

Zoubır Hanifi , Brahim Medjahdı

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.

Keywords

Lorentz-Heisenberg 3-space, Graph Translation Surface, Mean curvature, Gaussian curvature.

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