The Twisted Photon Associated to Hyper-Hermitian Four-Manifolds

Details The Twisted Photon Associated to Hyper-Hermitian Four-Manifolds The Twisted Photon Associated to Hyper-Hermitian Four-Manifolds

1998-08-31

arxiv.org/abs/math/9808137v1

J.Geom.Phys. 30 (1999) 266-281

Mathematics

Differential Geometry

12 pages, LaTex, no figures

Scientific paper

10.1016/S0393-0440(98)00060-6

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.

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