Twistorial harmonic morphisms with one-dimensional fibres on self-dual four-manifolds

Details Twistorial harmonic morphisms with one-dimensional fibres on self-dual four-manifolds Twistorial harmonic morphisms with one-dimensional fibres on self-dual four-manifolds

2003-05-07

arxiv.org/abs/math/0305110v3

Mathematics

Differential Geometry

39 pages, LaTeX 2e, using fancyheadings sty. Some minor improvements made. To appear in Q. J. Math

Scientific paper

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.

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