Partner symmetries, group foliation and ASD Ricci-flat metrics without Killing vectors

DOI10.3842/SIGMA.2013.075zbMath1290.35269arXiv1306.3195MaRDI QIDQ2447848

Andrei A. Malykh, Mikhail B. Sheftel

Publication date: 29 April 2014

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

Full work available at URL: https://arxiv.org/abs/1306.3195

zbMATH Keywords

Monge-Ampère equationRicci-flat metricsymmetry reductionBoyer-Finley equationgroup foliationanti-self-dual gravitynon-invariant solutionspartner symmetries

Mathematics Subject Classification ID

Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) PDEs in connection with relativity and gravitational theory (35Q75) Exact solutions to problems in general relativity and gravitational theory (83C15)

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Recursion operators and tri-Hamiltonian structure of the first heavenly equation of Plebański ⋮ Recursion operators and bi-Hamiltonian structure of the general heavenly equation ⋮ Nonlocal symmetry of CMA generates ASD Ricci-flat metric with no Killing vectors ⋮ Integrability of anti-self-dual vacuum Einstein equations with nonzero cosmological constant: an infinite hierarchy of nonlocal conservation laws ⋮ Exact solutions of semilinear radial Schrödinger equations by separation of group foliation variables

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