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

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-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.