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arXiv · 1604.03579

Metrisability of Painlevé equations

Felipe Contatto·Maciej Dunajski
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Abstract

We solve the metrisability problem for the six Painlevé equations, and more generally for all 2nd order ODEs with Painlevé property, and determine for which of these equations their integral curves are geodesics of a (pseudo) Riemannian metric on a surface.

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Felipe Contatto, Maciej Dunajski. 2018-02-05. Metrisability of Painlevé equations. https://arxiv.org/abs/1604.03579

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