Compact minimal surfaces in the Berger spheres

2010/07/07 by Francisco Torralbo, Torralbo, Francisco · 2 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Primary 53C42 #Secondary 53C30

paper · pdf · doi:10.48550/arxiv.1007.1072

openalex publication_date 2010/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We construct compact arbitrary Euler characteristic orientable and non-orientable minimal surfaces in the Berger spheres. Besides 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 the products S² x R, H² x R and in the Heisenberg group with many symmetries.

Citations

• Compact stable constant mean curvature surfaces in the Berger spheres

Cited by

• Minimal equators and homological systoles in Berger projective spaces
• Isometric immersions into three-dimensional unimodular metric Lie groups

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