Spherical metrics with conical singularities on a 2-sphere: angle constraints

Abstract

In this article we give a criterion for the existence of a metric of curvature $1$ on a $2$-sphere with $n$ conical singularities of prescribed angles $2\pi {\vartheta }_1,\dots ,2\pi {\vartheta }_n$ and non-coaxial holonomy. Such a necessary and sufficient condition is expressed in terms of linear inequalities in ${\vartheta }_1,\dots ,{\vartheta }_n$.

38 pages, 17 figures

References in corpus (1)

• Spherical quadrilaterals with three non-integer angles

Cited by in corpus (1)

• Hyperbolic 2-spheres with cone singularities