Scalar--flat Kähler metrics with conformal Bianchi V symmetry

Details Scalar--flat Kähler metrics with conformal Bianchi V symmetry Scalar--flat Kähler metrics with conformal Bianchi V symmetry

2010-10-14

arxiv.org/abs/1010.2963v2

Class.Quant.Grav.28:125004,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Dedicated to Maciej Przanowski on the occasion of his 65th birthday. Minor corrections. To appear in CQG

Scientific paper

10.1088/0264-9381/28/12/125004

We provide an affirmative answer to a question posed by Tod \cite{Tod:1995b}, and construct all four-dimensional Kahler 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(\infty) Toda equation by the existence a non-abelian two-dimensional group of point symmetries.

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