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arXiv · gr-qc/9803009

Einstein-Weyl structures and Bianchi metrics

Guy Bonneau
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Abstract

We analyse in a systematic way the (non-)compact four dimensional Einstein-Weyl spaces equipped with a Bianchi metric. We show that Einstein-Weyl structures with a Class A Bianchi metric have a conformal scalar curvature of constant sign on the manifold. Moreover, we prove that most of them are conformally Einstein or conformally Kähler ; in the non-exact Einstein-Weyl case with a Bianchi metric of the type $VII_0, VIII$ or $IX$, we show that the distance may be taken in a diagonal form and we obtain its explicit 4-parameters expression. This extends our previous analysis, limited to the diagonal, Kähler Bianchi $IX$ case.

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Guy Bonneau. 1998-06-12. Einstein-Weyl structures and Bianchi metrics. https://doi.org/10.1088/0264-9381%2F15%2F8%2F019

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