Article
A characterization of constant mean curvature surfaces in homogeneous 3-manifolds
Author/s | Fernández Delgado, Isabel
Mira, Pablo |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2007 |
Deposit Date | 2021-07-06 |
Published in |
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Abstract | 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. ... 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. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España |
Project ID. | MTM2004-00160
MTM2004-02746 |
Citation | Fernández Delgado, I. y Mira, P. (2007). A characterization of constant mean curvature surfaces in homogeneous 3-manifolds. Differential Geometry and its Applications, 25 (3), 281-289. |
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