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

Gabriele Mondello; Dmitri Panov

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arXiv · 1505.01994

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

Gabriele Mondello·Dmitri Panov

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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 $\vartheta_1,\dots,\vartheta_n$.

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BibTeX RIS

Gabriele Mondello, Dmitri Panov. 2015-05-08. Spherical metrics with conical singularities on a 2-sphere: angle constraints. https://arxiv.org/abs/1505.01994

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