Anti-Self-Dual Conformal Structures in Neutral Signature

Details Anti-Self-Dual Conformal Structures in Neutral Signature Anti-Self-Dual Conformal Structures in Neutral Signature

2006-10-09

arxiv.org/abs/math/0610280v5

Mathematics

Differential Geometry

48 pages, 1 figure, contribution to the special volume `Recent developments in pseudo-Riemannian Geometry', ESI-Series on Math

Scientific paper

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 Kahler condition and a twistor construction of a conformal structure with twisting null Killing vector - are new.

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