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Spheres with parallel mean curvature in $\mathbb{S}^{2}\times \mathbb{H}^{2}$

Year: 2026

Type: article

Abstract: 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.

Source: Revista Matemática Iberoamericana

DOI: 10.4171/rmi/1658

Authors: Giel Stas, Joeri Van der Veken

Institution: KU Leuven

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4416069233

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