Null Kähler structures, Symmetries and Integrability

Abstract

We review the integrable systems which arise as symmetry reductions of Plebanski's heavenly equations, and their generalisations. We also show that all four-dimensional null Kahler-Einstein (or type N hyper-heavenly) metrics with symmetry can be found from solutions to a variable coefficient generalisation of the dispersionless Kadomtsev-Petviashvili equation.

Text of a talk given at the conference on "Mathematical Physics, General Relativity and Cosmology", held in honour of Professor Jerzy Plebanski. To appear in the Proceedings