Darboux-Egoroff metrics, rational Landau-Ginzburg potentials and the Painleve VI equation

Abstract

We present a class of three-dimensional integrable structures associated with the Darboux-Egoroff metric and classical Euler equations of free rotations of a rigid body. They are obtained as canonical structures of rational Landau-Ginzburg potentials and provide solutions to the Painleve VI equation.