English

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