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

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.

arXiv comment24 pages, submitted to J. Phys. A: Math. Theor

References in corpus (5)

• Group foliation and non-invariant solutions of the heavenly equation
• Partner symmetries and non-invariant solutions of four-dimensional heavenly equations
• Gravitational instantons admit hyper-Kähler structure
• Partner symmetries of the complex Monge-Ampere equation yield hyper-Kahler metrics without continuous symmetries
• Anti-self-dual Riemannian metrics without Killing vectors, can they be realized on K3?

Cited by in corpus (7)

• Bi-Hamiltonian representation, symmetries and integrals of mixed heavenly and Husain systems
• On a class of second-order PDEs admitting partner symmetries
• Solutions of the sDiff(2)Toda equation with SU(2) Symmetry
• Recursions of Symmetry Orbits and Reduction without Reduction
• Lift of Invariant to Non-Invariant Solutions of Complex Monge-Ampère Equations
• Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors
• On some exact solutions of heavenly equations in four dimensions