Compact minimal surfaces in the Berger spheres

Abstract

In this article, we construct compact, arbitrary Euler characteristic, orientable and non-orientable minimal surfaces in the Berger spheres. Also, we show an interesting family of surfaces that are minimal in every Berger sphere, characterizing them by this property. Finally we construct, via the Daniel correspondence, new examples of constant mean curvature surfaces in \({\mathbb S^2 \times \mathbb R,\; \mathbb H^2 \times \mathbb R}\) and the Heisenberg group with many symmetries.