CMC-surfaces, flat structures and umbilical points

Details CMC-surfaces, flat structures and umbilical points CMC-surfaces, flat structures and umbilical points

2001-04-06

arxiv.org/abs/math/0104081v1

Buletinul Acad. de Sci. Moldova, Matematica 41 (2003), 83-90

Mathematics

Differential Geometry

Scientific paper

A short proof of the Caratheodory conjecture about index of an isolated
umbilic on the convex 2-dimensional sphere is suggested. The argument is based
on the study of geodesic lines near cone-type singularity of a metric induced
by holomorphic quadratic differentials.

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