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.

20 pages

References in corpus (3)

• Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy
• The construction of Frobenius manifolds from KP tau-functions
• Degenerate Frobenius manifolds and the bi-Hamiltonian structure of rational Lax equations