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arXiv · 0907.5541

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

Jose M. Espinar·Isabel Fernandez
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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.

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Jose M. Espinar, Isabel Fernandez. 2009-09-23. Totally umbilical disks and applications to surfaces in three-dimensional homogeneous spaces. https://arxiv.org/abs/0907.5541

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