Einstein-Weyl structures and Bianchi metrics

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 $VI{I}_0,VIII$ 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.

Latex file, 12 pages, a minor modification, accepted for publication in Class. Quant. Grav

References in corpus (1)

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

Cited by in corpus (3)

• Geometry of Quaternionic Kähler connections with torsion
• Compact Einstein-Weyl four-dimensional manifolds
• Cohomogeneity-one Einstein-Weyl structures : a local approach