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arXiv · 1311.2500

Compact embedded minimal surfaces in $\mathbb{S}^2\times \mathbb{S}^1$

José M. Manzano·Julia Plehnert·Francisco Torralbo
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Abstract

We prove that closed surfaces of all topological types, except for the non-orientable odd-genus ones, can be minimally embedded in the Riemannian product of a sphere and a circle of arbitrary radius. We illustrate it by obtaining some periodic minimal surfaces in $\mathbb{S}^2\times\mathbb{R}$ via conjugate constructions. The resulting surfaces can be seen as the analogy to the Schwarz P-surface in these homogeneous 3-manifolds.

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José M. Manzano, Julia Plehnert, Francisco Torralbo. 2013-11-11. Compact embedded minimal surfaces in $\mathbb{S}^2\times \mathbb{S}^1$. https://doi.org/10.4310/cag.2016.v24.n2.a7

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