Harmonic morphisms between Weyl spaces and twistorial maps

摘要

We show that Weyl spaces provide a natural context for harmonic morphisms, and we give the necessary and sufficient conditions under which on an Einstein-Weyl space of dimension 4 there can be defined, locally, at least five distinct foliations of dimension 2 which produce harmonic morphisms (Theorem 7.4). Also, we describe the harmonic morphisms between Einstein Weyl spaces of dimensions 4 and 3 (Theorem 7.6).