Geodesic
The Flat Translation Surfaces in the 3-Dimensional Lorentz Heisenberg Group H3
Journal for geometry and graphics, Tome 28 (2024) no. 1, pp. 1-18.

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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 $\mathbb{H}_3$.
Classification : 53A10, 53C30, 53C50, 53C42
Mots-clés : Gaussian curvature, Lorentz Heisenberg space, first fundamental form, second fundamental form, translation surface, flat surface 
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R. Medjati; S. Taifour; H. Zoubir . The Flat Translation Surfaces in the 3-Dimensional Lorentz Heisenberg Group H3. Journal for geometry and graphics, Tome 28 (2024) no. 1, pp. 1-18. http://geodesic.mathdoc.fr/item/JGG_2024_28_1_JGG_2024_28_1_a0/