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29 March 2020
  » arxiv » 1010.2963

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Scalar--flat K"ahler metrics with conformal Bianchi V symmetry
Maciej Dunajski ; Prim Plansangkate ;
Date 14 Oct 2010
AbstractWe 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.
Source arXiv, 1010.2963
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