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

References in corpus (2)

• A class of Einstein--Weyl spaces associated to an integrable system of hydrodynamic type
• Einstein--Weyl spaces and dispersionless Kadomtsev--Petviashvili equation from Painlevé I and II

Cited by in corpus (3)

• The Geometry of Almost Einstein (2,3,5) Distributions
• Conformal geometry and half-integrable spacetimes
• Lie symmetries of a generalized Kuznetsov-Zabolotskaya-Khoklov equation