Spherical Metrics with Conical Singularities on a 2-Sphere: Angle Constraints

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 |2π ϑ ₁,… ,2π ϑ ₙ| and non-coaxial holonomy. Such a necessary and sufficient condition is expressed in terms of linear inequalities in |ϑ ₁,… ,ϑ ₙ|⁠.