Journal for Geometry and Graphics 28 (2024), No. 1, 001--018
Copyright by the authors licensed under CC BY SA 4.0
The Flat Translation Surfaces in the 3-Dimensional Lorentz Heisenberg Group H3
Rafik Medjati
ENP Oran - Maurice AUDIN (Ex ENSET), El-Mnaouer, Oran, Algeria
rafik.medjati@enp-oran.dz
Said Taifour
ENP Oran - Maurice AUDIN (Ex ENSET), El-Mnaouer, Oran, Algeria
said.taifur@enp-oran.dz
Hanifi Zoubir
ENP Oran - Maurice AUDIN (Ex ENSET), El-Mnaouer, Oran, Algeria
zoubirhanifi@yahoo.fr
[Abstract-pdf]
In the Lorentz-Heisenberg space $\mathbb{H}_3$ endowed with flat metric $g_3$, a translation surface is parametrized by $r(x,y) = \gamma_1(x) * \gamma_2(y)$, where $\gamma_1$ and $\gamma_2$ are two planar curves lying in planes, which are not orthogonal. In this article, we classify translation surfaces in $\mathbb{H}_3$, with vanishing Gaussian curvature in Lorentz-Heisenberg space $\mathbb{H}_3$.
Keywords: Gaussian curvature, Lorentz Heisenberg space, first fundamental form, second fundamental form, translation surface, flat surface.
MSC: 53A10; 53C30, 53C50, 53C42.
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