A characterization of constant mean curvature surfaces in homogeneous 3-manifolds
It has been recently shown by Abresch and Rosenberg that a cer- tain Hopf differential is holomorphic on every constant mean curvature surface in a Riemannian homogeneous 3-manifold with isometry group of dimension 4. In this paper we describe all the surfaces with holomorphic Hopf differential in t...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/115194 |
| Acceso en línea: | https://hdl.handle.net/11441/115194 https://doi.org/10.1016/j.difgeo.2006.11.006 |
| Access Level: | acceso abierto |
| Palabra clave: | Constant mean curvature Hopf differential Homogeneous manifolds Berger spheres |
| Sumario: | It has been recently shown by Abresch and Rosenberg that a cer- tain Hopf differential is holomorphic on every constant mean curvature surface in a Riemannian homogeneous 3-manifold with isometry group of dimension 4. In this paper we describe all the surfaces with holomorphic Hopf differential in the homogeneous 3-manifolds isometric to H2 ×R or having isometry group isomorphic either to the one of the universal cover of PSL(2, R), or to the one of a certain class of Berger spheres. It turns out that, except for the case of these Berger spheres, there exist some exceptional surfaces with holomorphic Hopf differential and non-constant mean curvature. |
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