Einstein-Weyl structures and Bianchi metrics

Details Einstein-Weyl structures and Bianchi metrics Einstein-Weyl structures and Bianchi metrics

1998-03-02

arxiv.org/abs/gr-qc/9803009v2

Class.Quant.Grav. 15 (1998) 2415-2425

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1088/0264-9381/15/8/019

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 K\"ahler ; 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, K\"ahler Bianchi $IX$ case.

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