Recent Developments in Pseudo-Riemannian Geometry

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pp: 113–148

DOI: 10.4171/051-1/4

Anti-self-dual conformal structures in neutral signature

Maciej Dunajski[1] and Simon West[2]

(1) University of Cambridge, UK
(2) University of Cambridge, UK

We review the subject of four dimensional anti-self-dual conformal structures with signature (++−−). Both local and global questions are discussed. Most of the material is well known in the literature and we present it in a way which underlines the connection with integrable systems. Some of the results – e.g. the Lax pair characterisation of the scalar-flat K√§hler condition and a twistor construction of a conformal structure with twisting null Killing vector – are new.

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