A characterization of constant mean curvature surfaces in homogeneous 3-manifolds |
| |
Authors: | Isabel Fernández Pablo Mira |
| |
Institution: | a Departamento de Geometría y Topología, Universidad de Granada, E-18071 Granada, Spain b Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, E-30203 Cartagena, Murcia, Spain |
| |
Abstract: | It has been recently shown by Abresch and Rosenberg that a certain 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. |
| |
Keywords: | 53A10 53C42 |
本文献已被 ScienceDirect 等数据库收录! |
|