English

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}
}