arXiv subjects
Publications and source records attributed to Christiam Figueroa.
In this paper, we establish a complete classification of minimal translation surfaces within the 3-dimensional Heisenberg group $\mathcal{H}_3$. While translation surfaces in $\mathcal{H}_3$ yield diverse families of solutions depending on the choice of generating curves, we prove that, up to isometries of $\mathcal{H}_3$, there exists a unique class of translation surfaces.
A translation surface in the Heisenberg group is constructed as the product of two planar curves. We classify a type of such surfaces with vanishing intrinsic curvature by analyzing the determinant of their Gauss map
In this paper, we study the Gauss map of surfaces in 3-dimensional Heisenberg group using the Gans model of the hyperbolic plane. We establish a relationship between the tension field of the Gauss map and mean curvature of a surface in $\mathcal{H}_{3}$.
In this paper we study some geometric properties of surfaces in the Heisenberg group, $\mathcal{H}_{3}.$ We obtain, using the Gauss map for Lie groups, a partial classification of minimal graphs in $\mathcal{H}_{3}.$ We also proof the non existence of umbilical surfaces in $\mathcal{H}_{3}.$