Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606691 | Differential Geometry and its Applications | 2007 | 9 Pages |
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×RH2×R or having isometry group isomorphic either to the one of the universal cover of PSL(2,R)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
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Isabel Fernández, Pablo Mira,