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 2πθ1,...,2πθn and non-coaxial holonomy. Such a necessary and sufficient condition is expressed in terms of linear inequalities in θ1,...,θn.
Spherical metrics with conical singularities on a 2-sphere: angle constraints / Mondello, Gabriele; Panov, Dmitri. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - STAMPA. - 16:(2016), pp. 4937-4995. [10.1093/imrn/rnv300]
Spherical metrics with conical singularities on a 2-sphere: angle constraints
MONDELLO, GABRIELE;
2016
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 2πθ1,...,2πθn and non-coaxial holonomy. Such a necessary and sufficient condition is expressed in terms of linear inequalities in θ1,...,θn.File allegati a questo prodotto
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