Metrics of positive curvature with conic singularities on the sphere

Details Metrics of positive curvature with conic singularities on the sphere Metrics of positive curvature with conic singularities on the sphere

2002-08-04

arxiv.org/abs/math/0208025v1

Proc. AMS, 132 (2004), 11, 3349--3355

Mathematics

Metric Geometry

9 pages, 1 figure, LaTeX

Scientific paper

A simple proof is given of the necessary and sufficient condition on a triple
of positive numbers A,B,C for the existence of a conformal metric of constant
positive curvature on the sphere, with three conic singularities of total
angles A,B,C. The same condition is necessary and sufficient for the triple
A,B,C to be interior angles of a spherical triangular membrane.

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