Totally umbilical disks and applications to surfaces in three-dimensional homogeneous spaces
Differential Geometry
2009-09-23 v3
Abstract
Following ideas of Choe and Fernandez-do Carmo, we give sufficient conditions for a disk type surface, with piecewise smooth boundary, to be totally umbilical for a given Coddazi pair. As a consequence, we obtain rigidity results for surfaces in space forms and in homogeneous product spaces that generalizes some known results.
Keywords
Cite
@article{arxiv.0907.5541,
title = {Totally umbilical disks and applications to surfaces in three-dimensional homogeneous spaces},
author = {Jose M. Espinar and Isabel Fernandez},
journal= {arXiv preprint arXiv:0907.5541},
year = {2009}
}