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Cohomogeneity-one Einstein-Weyl structures : a local approach | | Guy Bonneau
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16 Dec 1999 | | Journal: | J.Geom.Phys. 39 (2001) 135-173 | | Subject: | General Relativity and Quantum Cosmology; Differential Geometry; Mathematical Physics | gr-qc math-ph math.DG math.MP | | Affiliation: | LPTHE, Paris | | Abstract: | 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 Kähler metrics, the (n-2)-dimensional space G/(HxH’) being an arbitrary compact symmetric Kähler coset space. | | Source: | arXiv, gr-qc/9912067 | | Services: | Forum | Review | PDF | Favorites | |
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