Twistorial harmonic morphisms with one-dimensional fibres on self-dual four-manifolds
Abstract
Description
We introduce a general notion of twistorial map and classify twistorial harmonic morphisms with one-dimensional fibres from self-dual four-manifolds. Such maps can be characterised as those which pull back Abelian monopoles to self-dual connections. In fact, the constructions involve solving a generalised monopole equation, and also the Beltrami fields equation of hydrodynamics, and lead to constructions of self-dual metrics.
39 pages, LaTeX 2e, using fancyheadings sty. Some minor improvements made. To appear in Q. J. Math
39 pages, LaTeX 2e, using fancyheadings sty. Some minor improvements made. To appear in Q. J. Math