2025/09/10 by Giel Stas, Stas, Giel, Joeri Van der Veken +1
Mathematics · #53A10 (Primary) 53C40 (Secondary) #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2509.08581
openalex publication_date 2025/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that a surface with parallel mean curvature vector field in a Riemannian product of two surfaces of constant Gaussian curvature carries a holomorphic quadratic differential. In this paper we consider the Riemannian product of a sphere and a hyperbolic plane of opposite Gaussian curvatures and study the parallel mean curvature surfaces for which the differential vanishes. In particular, we classify all parallel mean curvature spheres, for which the differential vanishes for topological reasons.