By Magri's theorem, self-dual gravity is completely integrable

DOI10.3842/SIGMA.2007.034zbMATH Open1136.83314arXivnlin/0702055MaRDI QIDQ2473430

Publication date: 27 February 2008

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Abstract: By Magri's theorem the bi-Hamiltonian structure of Plebanski's second heavenly equation proves that (anti)-self-dual gravity is a completely integrable system in four dimensions.

Full work available at URL: https://arxiv.org/abs/nlin/0702055

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zbMATH Keywords

self-dual gravity Plebanski equation Magri's theorem

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory (83C20) Exact solutions to problems in general relativity and gravitational theory (83C15)

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