Spheres with parallel mean curvature in $\mathbb{S}^2 \times \mathbb{H}^2$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916944902356992 |
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| author | Stas, Giel Van der Veken, Joeri |
| author_facet | Stas, Giel Van der Veken, Joeri |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_08581 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spheres with parallel mean curvature in $\mathbb{S}^2 \times \mathbb{H}^2$ Stas, Giel Van der Veken, Joeri Differential Geometry 53C42, 53A10 (Primary) 53C40 (Secondary) 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. |
| title | Spheres with parallel mean curvature in $\mathbb{S}^2 \times \mathbb{H}^2$ |
| topic | Differential Geometry 53C42, 53A10 (Primary) 53C40 (Secondary) |
| url | https://arxiv.org/abs/2509.08581 |