Scalar--flat K\"ahler metrics with conformal Bianchi V symmetry
Abstract
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.
Keywords
Cite
@article{arxiv.1010.2963,
title = {Scalar--flat K\"ahler metrics with conformal Bianchi V symmetry},
author = {Maciej Dunajski and Prim Plansangkate},
journal= {arXiv preprint arXiv:1010.2963},
year = {2011}
}
Comments
Dedicated to Maciej Przanowski on the occasion of his 65th birthday. Minor corrections. To appear in CQG