Lift of noninvariant solutions of heavenly equations from three to four dimensions and new ultra-hyperbolic metrics

DOI10.1088/1751-8113/40/31/014zbMATH Open1127.35069arXiv0704.3335OpenAlexW2020046169MaRDI QIDQ5757599

Mikhail B. Sheftel, Y. Nutku, Andrei A. Malykh

Publication date: 7 September 2007

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Abstract: We demonstrate that partner symmetries provide a lift of noninvariant solutions of three-dimensional Boyer-Finley equation to noninvariant solutions of four-dimensional hyperbolic complex Monge-Ampere equation. The lift is applied to noninvariant solutions of the Boyer-Finley equation, obtained earlier by the method of group foliation, to yield noninvariant solutions of the hyperbolic complex Monge-Ampere equation. Using these solutions we construct new Ricci-flat ultra-hyperbolic metrics with non-zero curvature tensor that have no Killing vectors.

Full work available at URL: https://arxiv.org/abs/0704.3335

zbMATH Keywords

complex Monge-Ampère equationBoyer-Finley equationRicci-flat ultra-hyperbolic metrics with non-zero curvature tensor

Mathematics Subject Classification ID

PDEs in connection with relativity and gravitational theory (35Q75) Exact solutions to problems in general relativity and gravitational theory (83C15)

Related Items (3)

Recursion operators and bi-Hamiltonian structure of the general heavenly equation ⋮ Lift of Invariant to Non-Invariant Solutions of Complex Monge-Ampère Equations ⋮ Bi-Hamiltonian Representation, Symmetries and Integrals of Mixed Heavenly and Husain Systems

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