Spheres with parallel mean curvature in $\mathbb{S}^2 \times \mathbb{H}^2$
Differential Geometry
2025-09-11 v1
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.
Cite
@article{arxiv.2509.08581,
title = {Spheres with parallel mean curvature in $\mathbb{S}^2 \times \mathbb{H}^2$},
author = {Giel Stas and Joeri Van der Veken},
journal= {arXiv preprint arXiv:2509.08581},
year = {2025}
}
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17 pages