Traslation surfaces in the Heisenberg Group

TL;DR

This paper classifies translation surfaces in the Heisenberg group with zero intrinsic curvature, using the determinant of their Gauss map to analyze their geometric properties.

Contribution

It provides a classification of a specific type of translation surfaces in the Heisenberg group with vanishing intrinsic curvature, expanding understanding of their geometric structure.

Findings

Classification of translation surfaces with zero intrinsic curvature

Use of Gauss map determinant in geometric analysis

Explicit characterization of such surfaces in the Heisenberg group

Abstract

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