Einstein-Weyl structures corresponding to diagonal Kähler Bianchi IX metrics

Details Einstein-Weyl structures corresponding to diagonal Kähler Bianchi IX metrics Einstein-Weyl structures corresponding to diagonal Kähler Bianchi IX metrics

1996-12-05

arxiv.org/abs/hep-th/9612055v2

Class.Quant.Grav. 14 (1997) 2123-2135

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, Latex file, minor modifications, to be published in Class. Quant. Grav

Scientific paper

10.1088/0264-9381/14/8/012

We analyse in a systematic way the four dimensionnal Einstein-Weyl spaces equipped with a diagonal K\"ahler Bianchi IX metric. In particular, we show that the subclass of Einstein-Weyl structures with a constant conformal scalar curvature is the one with a conformally scalar flat - but not necessarily scalar flat - metric ; we exhibit its 3-parameter distance and Weyl one-form. This extends previous analysis of Pedersen, Swann and Madsen , limited to the scalar flat, antiself-dual case. We also check that, in agreement with a theorem of Derdzinski, the most general conformally Einstein metric in the family of biaxial K\"ahler Bianchi IX metrics is an extremal metric of Calabi, conformal to Carter's metric, thanks to Chave and Valent's results.

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