Cohomogeneity-one Einstein-Weyl structures : a local approach

Details Cohomogeneity-one Einstein-Weyl structures : a local approach Cohomogeneity-one Einstein-Weyl structures : a local approach

1999-12-16

arxiv.org/abs/gr-qc/9912067v3

J.Geom.Phys. 39 (2001) 135-173

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

36 pages, Latex file, corrections in some definitions and terminology, no change in results, final version to appear in `` Jou

Scientific paper

We analyse in a systematic way the (non-)compact n-dimensional Einstein Weyl spaces equipped with a cohomogeneity-one metric. With no compactness hypothesis, we prove that, as soon as the (n-1)-dimensional space is an homogeneous reductive Riemannian space with an unimodular group of left-acting isometries G 1)a non-exact Einstein-Weyl stucture may exist only if the (n-1)-dimensional homogeneous space G/H contains a non trivial subgroup H' that commutes with the isotropy subgroup H, 2) the extra isometry due to this Killing vector corresponds to the right-action of one of the generators of the algebra of the subgroup H'. We also prove that the subclass with a one-dimensional subgroup H' corresponds to n-dimensional Riemannian locally conformally K\"ahler metrics, the (n-2)-dimensional space G/(HxH') being an arbitrary compact symmetric K\"ahler coset space.

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