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The Twisted Photon Associated to Hyper-Hermitian Four-Manifolds

Maciej Dunajski
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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.

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BibTeXRIS

Maciej Dunajski. 1998-08-31. The Twisted Photon Associated to Hyper-Hermitian Four-Manifolds. https://doi.org/10.1016/s0393-0440(98)00060-6

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