Einstein-Weyl structures and Bianchi metrics
Guy Bonneau
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 VII0, 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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