Totally umbilical disks and applications to surfaces in three-dimensional homogeneous spaces

Abstract

Following [Ch] and [dCF], 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.Ministerio de Educación y Ciencia MTM2007-65249Ministerio de Educación y Ciencia MTM2007-64504Junta de Andalucía P06-FQM-01642Junta de Andalucía FQM32