Einstein - Weyl structures and Bianchi metrics
نویسندگان
چکیده
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 Kahler ; in the non-exact Einstein-Weyl case with a Bianchi metric of the type V II0 ; V III 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, Kahler Bianchi IX case. PAR/LPTHE/98-06/gr-qc/9803009 February 1998 Laboratoire de Physique Th eorique et des Hautes Energies, Unit e associ ee au CNRS URA 280, Universit e Paris 7, 2 Place Jussieu, 75251 Paris Cedex 05. [email protected]
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