Co-axial monodromy

Abstract

For Riemannian metrics of constant positive curvature on a punctured sphere with conic singularities at the punctures and co-axial monodromy of the developing map, possible angles at the singularities are completely described. This completes the recent result of Mondello and Panov. The related problem of describing possible multiplicities of critical points of logarithmic potentials of finitely many charges is also solved.