Abstract
We demonstrate that partner symmetries provide a lift of noninvariant solutions of the three-dimensional Boyer–Finley equation to noninvariant solutions of the four-dimensional hyperbolic complex Monge–Ampère 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–Ampère 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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