On complete constant mean curvature vertical multigraphs in E(\kappa,\tau)
Differential Geometry
2015-03-02 v2
Abstract
We prove that any complete surface with constant mean curvature in a homogeneous space E(\kappa,\tau) which is transversal to the vertical Killing vector field is, in fact, a vertical graph. As a consequence we get that any orientable, parabolic, complete, immersed surface with constant mean curvature H in E(\kappa,\tau) (different from a horizontal slice in S^2xR) is either a vertical cylinder or a vertical graph (in both cases, it must be 4H^2+\kappa\leq0).
Cite
@article{arxiv.1206.1578,
title = {On complete constant mean curvature vertical multigraphs in E(\kappa,\tau)},
author = {José M. Manzano and M. Magdalena Rodríguez},
journal= {arXiv preprint arXiv:1206.1578},
year = {2015}
}
Comments
11 pages, 2 figures