Minimal translation surfaces in the Heisenberg group Nil3

TL;DR

This paper classifies all minimal translation surfaces in the Heisenberg group Nil3, providing a complete geometric characterization of these surfaces constructed via group multiplication of two curves.

Contribution

It offers the first complete classification of minimal translation surfaces in Nil3, advancing understanding of minimal surfaces in sub-Riemannian geometry.

Findings

Complete classification of minimal translation surfaces in Nil3

Explicit descriptions of the surfaces constructed from two curves

New insights into the geometry of minimal surfaces in Heisenberg groups

Abstract

A translation surface in the Heisenberg group $\mathrm{Nil}_3$ is a surface constructed by multiplying (using the group operation) two curves. We completely classify minimal translation surfaces in the Heisenberg group $\mathrm{Nil}_3$.