Differential invariants of Einstein-Weyl structures in 3D

Abstract

Einstein–Weyl structures on a three-dimensional manifold <i>M</i> are given by a system <i>E</i> of PDEs on sections of a bundle over <i>M</i>. This system is invariant under the Lie pseudogroup <i>G</i> of local diffeomorphisms on <i>M</i>. Two Einstein–Weyl structures are locally equivalent if there exists a local diffeomorphism taking one to the other. Our goal is to describe the quotient equation <i>E/G</i> whose solutions correspond to nonequivalent Einstein–Weyl structures. The approach uses symmetries of the Manakov–Santini integrable system and the action of the corresponding Lie pseudogroup.