A characterization of constant mean curvature surfaces in homogeneous 3-manifolds

Simple item page
dc.creatorFernandez, Isabel
dc.creatorMira, Pablo
dc.date2005-12-13
dc.date2006-01-10
dc.date.accessioned2026-07-07T06:55:09Z
dc.date.available2026-07-07T06:55:09Z
dc.descriptionIt 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.
dc.descriptioncorrected typos
dc.identifierhttps://arxiv.org/abs/math/0512280
dc.identifierhttp://arxiv.org/abs/math/0512280
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106191
dc.subjectDifferential Geometry
dc.subject53A10; 53C42
dc.titleA characterization of constant mean curvature surfaces in homogeneous 3-manifolds
dc.typetext

Files

Collections

arXiv