Surfaces in Sol$_3$ space foliated by circles
Differential Geometry
2014-10-10 v1
Abstract
In this paper we study surfaces foliated by a uniparametric family of circles in the homogeneous space Sol. We prove that there do not exist such surfaces with zero mean curvature or with zero Gaussian curvature. We extend this study considering surfaces foliated by geodesics, equidistant lines or horocycles in totally geodesic planes and we classify all such surfaces under the assumption of minimality or flatness.
Cite
@article{arxiv.1410.2513,
title = {Surfaces in Sol$_3$ space foliated by circles},
author = {Rafael López and Ana Nistor},
journal= {arXiv preprint arXiv:1410.2513},
year = {2014}
}