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

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

2009-07-31

arxiv.org/abs/0907.5541v3

Mathematics

Differential Geometry

Scientific paper

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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