Minimal surfaces in the product of two dimensional real space forms endowed with a neutral metric

2016/03/12 by Martha P. Dussan, Dussan, Martha P., Nikos Georgiou +4
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1603.03877

arxiv created 2016/03/12 · openalex publication_date 2016/03/12 · arxiv updated 2016/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate minimal surfaces in products of two-spheres \mathbb S²_p× \mathbb S²_p, with the neutral metric given by (g,-g). Here \mathbb S²_p⊂ \mathbb R^p,3-p , and g is the induced metric on the sphere. We compute all totally geodesic surfaces and we give a relation between minimal surfaces and the solutions of the Gordon equations. Finally, in some cases we give a topological classification of compact minimal surfaces.

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