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Compact minimal surfaces in the Berger spheres

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Abstract

In this article, we construct compact, arbitrary Euler characteristic, orientable and non-orientable minimal surfaces in the Berger spheres. Also, we show an interesting family of surfaces that are minimal in every Berger sphere, characterizing them by this property. Finally we construct, via the Daniel correspondence, new examples of constant mean curvature surfaces in \({\mathbb S^2 \times \mathbb R,\; \mathbb H^2 \times \mathbb R}\) and the Heisenberg group with many symmetries.

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Authors and Affiliations

  1. Departamento de Geometría y Topología, Universidad de Granada, 18071, Granada, Spain

    Francisco Torralbo

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  1. Francisco Torralbo
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Correspondence to Francisco Torralbo.

Additional information

Research partially supported by a MCyT-Feder research project MTM2007-61775 and a Junta Andalucía Grant P06-FQM-01642.

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Torralbo, F. Compact minimal surfaces in the Berger spheres. Ann Glob Anal Geom 41, 391–405 (2012). https://doi.org/10.1007/s10455-011-9288-7

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  • DOI: https://doi.org/10.1007/s10455-011-9288-7

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