arXiv subjects

Tarcios Andrey Ferreira

Publications and source records attributed to Tarcios Andrey Ferreira.

3 recordsLinked to original sources

arXiv2026

Homogeneous Hypersurfaces in 4-dimensional Thurston Geometries with 4-dimensional Isometry Group

We classify, up to conjugacy, the 3-dimensional subalgebras of the Lie algebras associated with the 4-dimensional Thurston geometries whose isometry groups have dimension 4. Since homogeneous hypersurfaces arise as orbits of subgroups of the isometry group acting transitively on the ambient space, we determine all such subgroups and describe their corresponding orbits, thereby obtaining a classification of the homogeneous hypersurfaces, up to ambient isometries, and we study the geometry of the orbit foliations in these geometries.

math.DG↗

arXiv2026

Classification of Minimal Surfaces and Solitons to the Mean Curvature Flow in $\mathbb{H}^3$ as Translation Surfaces

We consider the hyperbolic three-space in the half-space model endowed with a metric Lie group structure. In this setting, translation surfaces are defined as products of two curves $α$ and $β$ with respect to the Lie group operation. We investigate minimal surfaces and solitons to the mean curvature flow arising from specific types of products of these curves. In particular, we provide classification results for minimal surfaces, hyperbolic translators, and conformal solitons to the mean curvature flow.

math.DG↗

arXiv2025

Rigidity of Translation Surfaces in the Three-Dimensional Sphere $\mathbb{S}^3$

A translation surface in the three-dimensional sphere $\mathbb{S}^3$ is a surface generated by the quaternionic product of two curves, called generating curves. In this paper, we present rigidity results for such surfaces. We introduce an associated frame for curves in $\mathbb{S}^3$, and by means of it, we describe the local intrinsic and extrinsic geometry of translation surfaces in $\mathbb{S}^3$. The rigidity results, concerning minimal and constant mean curvature surfaces, are given in terms of the curvature and torsion of the generating curves and their proofs rely on the associated frame of such curves. Finally, we present a correspondence between translation surfaces in $\mathbb{S}^3$ and translation surfaces in $\mathbb{R}^3$. We show that these surfaces are locally isometric, and we present a relation between their mean curvatures.

math.DG↗