Twistorial harmonic morphisms with one-dimensional fibres on self-dual four-manifolds
Differential Geometry
2007-05-23 v3
Abstract
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.
Keywords
Cite
@article{arxiv.math/0305110,
title = {Twistorial harmonic morphisms with one-dimensional fibres on self-dual four-manifolds},
author = {R. Pantilie and J. C. Wood},
journal= {arXiv preprint arXiv:math/0305110},
year = {2007}
}
Comments
39 pages, LaTeX 2e, using fancyheadings sty. Some minor improvements made. To appear in Q. J. Math