Invariant minimal surfaces in the real special linear group of degree 2

TL;DR

This paper studies invariant minimal surfaces in the real special linear group of degree 2, classifying constant mean curvature surfaces with vertically harmonic Gauss maps under Riemannian and Lorentzian metrics.

Contribution

It provides a classification of constant mean curvature surfaces with vertically harmonic Gauss maps in this geometric setting.

Findings

Classification of invariant minimal surfaces under specified metrics

Identification of conditions for constant mean curvature surfaces

Analysis of Gauss map harmonicity in the context

Abstract

Invariant minimal surfaces in the real special linear group of degree 2 with canonical Riemannian and Lorentzian metrics are studied. Constant mean curvature surfaces with vertically harmonic Gau{\ss} map are classified.