The Twisted Photon Associated to Hyper-Hermitian Four-Manifolds
Differential Geometry
2009-10-31 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
solv-int
Abstract
The Lax formulation of the hyper-Hermiticity condition in four dimensions is used to derive a potential that generalises Plebanski's second heavenly equation for hyper-Kahler 4-manifolds. A class of examples of hyper-Hermitian metrics which depend on two arbitrary functions of two complex variables is given. The twistor theory of four-dimensional hyper-Hermitian manifolds is formulated as a combination of the Nonlinear Graviton Construction with the Ward transform for anti-self-dual Maxwell fields.
Cite
@article{arxiv.math/9808137,
title = {The Twisted Photon Associated to Hyper-Hermitian Four-Manifolds},
author = {Maciej Dunajski},
journal= {arXiv preprint arXiv:math/9808137},
year = {2009}
}
Comments
12 pages, LaTex, no figures