LAUSR

Abstract Einstein–Weyl structures on a three-dimensional manifold M are given by a system E of PDEs on sections of a bundle over M . This system is invariant under the Lie pseudogroup G of local diffeomorphisms on M . 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 E ∕ G 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.