Surfaces de Bonnet et \'equations de Painlev\'e
Mathematical Physics
2017-10-16 v2 Differential Geometry
math.MP
Exactly Solvable and Integrable Systems
Abstract
Nous montrons que les \'equations du rep\`ere mobile des surfaces de Bonnet conduisent \`a une paire de Lax matricielle isomonodromique d'ordre deux pour la sixi\`eme \'equation de Painlev\'e. We show that the moving frame equations of Bonnet surfaces can be extrapolated to a second order, isomonodromic matrix Lax pair of the sixth Painlev\'e equation.
Cite
@article{arxiv.1607.01222,
title = {Surfaces de Bonnet et \'equations de Painlev\'e},
author = {Robert Conte},
journal= {arXiv preprint arXiv:1607.01222},
year = {2017}
}
Comments
in French. Formula (14) added. Two paragraphs added p 5-6. Old ref 1 removed, ref 7 added. To appear, Comptes rendus Acad. sciences Paris