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arXiv · gr-qc/9806037

Compact Einstein-Weyl four-dimensional manifolds

Guy Bonneau
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Abstract

We look for four dimensional Einstein-Weyl spaces equipped with a regular Bianchi metric. Using the explicit 4-parameters expression of the distance obtained in a previous work for non-conformally-Einstein Einstein-Weyl structures, we show that only four 1-parameter families of regular metrics exist on orientable manifolds : they are all of Bianchi $IX$ type and conformally Kähler ; moreover, in agreement with general results, they have a positive definite conformal scalar curvature. In a Gauduchon's gauge, they are compact and we obtain their topological invariants. Finally, we compare our results to the general analyses of Madsen, Pedersen, Poon and Swann : our simpler parametrisation allows us to correct some of their assertions.

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Guy Bonneau. 1998-11-04. Compact Einstein-Weyl four-dimensional manifolds. https://doi.org/10.1088/0264-9381%2F16%2F3%2F031

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