A characterization of constant mean curvature surfaces in homogeneous 3-manifolds
Differential Geometry
2007-05-23 v3
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 H^2xR 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
Cite
@article{arxiv.math/0512280,
title = {A characterization of constant mean curvature surfaces in homogeneous 3-manifolds},
author = {Isabel Fernandez and Pablo Mira},
journal= {arXiv preprint arXiv:math/0512280},
year = {2007}
}
Comments
corrected typos