Metrisability of Painlevé equations
arXiv:1604.03579
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.
arXiv comment10 pages. Final version, minor revisions. To appear in JMP