Scalar-flat Kähler metrics with conformal Bianchi V symmetryDedicated to Maciej Przanowski on the occasion of his 65th birthday.

Maciej Dunajski (1, 2) , Prim Plansangate (3)

1 DAMTP - Department of Applied Mathematics and Theoretical Physics
2 Institute of Mathematics
3 UdeM - Université de Montréal

We provide an affirmative answer to a question posed by Tod [ 19 ], and construct all four-dimensional Kähler metrics with vanishing scalar curvature which are invariant under the conformal action of Bianchi V group. The construction is based on the combination of twistor theory and the isomonodromic problem with two double poles. The resulting metrics are non-diagonal in the left-invariant basis and are explicitly given in terms of Bessel functions and their integrals. We also make a connection with the LeBrun ansatz, and characterise the associated solutions of the SU (∞) Toda equation by the existence a non-abelian two-dimensional group of point symmetries.

Mots clés: Physical Sciences

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

Maciej Dunajski, Prim Plansangate. Scalar-flat Kähler metrics with conformal Bianchi V symmetryDedicated to Maciej Przanowski on the occasion of his 65th birthday.. Classical and Quantum Gravity, 2011, 28 (12), pp.125004. ⟨10.1088/0264-9381/28/12/125004⟩. ⟨hal-00710465⟩