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arXiv · 0704.3335

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
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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.

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A. A. Malykh, Y. Nutku, M. B. Sheftel. 2007-05-05. Lift of noninvariant solutions of heavenly equations from three to four dimensions and new ultra-hyperbolic metrics. https://doi.org/10.1088/1751-8113/40/31/014

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