Minimal translation surfaces in the Heisenberg group Nil3

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 ${\mathrm{Nil}}_3$.

10 pages

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• Minimal translation surfaces with respect to semi-symmetric connections in ${\mathbb{R}}^3$ and ${\mathbb{R}}_1^3$
• Asymptotic and exterior Dirichlet problems for the minimal surface equation in the Heisenberg group with a balanced metric
• Minimal surfaces with non-trivial topology in the three-dimensional Heisenberg group