Metrisability of Painlev\'e equations
Differential Geometry
2018-02-06 v2 High Energy Physics - Theory
Exactly Solvable and Integrable Systems
Abstract
We solve the metrisability problem for the six Painlev\'e equations, and more generally for all 2nd order ODEs with Painlev\'e property, and determine for which of these equations their integral curves are geodesics of a (pseudo) Riemannian metric on a surface.
Cite
@article{arxiv.1604.03579,
title = {Metrisability of Painlev\'e equations},
author = {Felipe Contatto and Maciej Dunajski},
journal= {arXiv preprint arXiv:1604.03579},
year = {2018}
}
Comments
10 pages. Final version, minor revisions. To appear in JMP