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20 April 2024

» arxiv » arxiv.0704.3335

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Lift of noninvariant solutions of heavenly equations from three to four dimensions and new ultra-hyperbolic metrics
A. A. Malykh ; Y. Nutku ; M. B. Sheftel ;
Date:	25 Apr 2007
Subject:	Mathematical Physics (math-ph)
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.
Source:	arXiv, arxiv.0704.3335
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