Darboux-Egoroff Metrics, Rational Landau-Ginzburg Potentials and the   Painleve VI Equation
  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. 
H. Aratyn, J.F. Gomes and A.H. Zimerman