Darboux-Egoroff Metrics, Rational Landau-Ginzburg Potentials and the Painleve VI Equation

TL;DR

This paper introduces a class of integrable structures linked to Darboux-Egoroff metrics and Landau-Ginzburg potentials that yield solutions to the Painleve VI equation, advancing understanding in integrable systems.

Contribution

It establishes a novel connection between Darboux-Egoroff metrics, rational Landau-Ginzburg potentials, and solutions to the Painleve VI equation.

Findings

New integrable structures associated with Darboux-Egoroff metrics

Explicit solutions to Painleve VI from Landau-Ginzburg potentials

Linking classical Euler equations with integrable systems

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.