ISSN:
1572-9060
Keywords:
conformal geometry
;
Einstein–Weyl
;
homogeneous
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Following an earlier study [3], we consider the Einstein–Weyl equations on a fixed (complex) background metric as an equation for a 1-form and its first few derivatives. If the background is flat then we conclude that the only solutions are conformal rescalings of constant curvature metrics. If the background is a homogeneous 3-geometry in Bianchi class A (i.e., with unimodular isometry group), we find necessary and sufficient conditions on the 3-geometry for solutions of the Einstein–Weyl equations to exist. The solutions we find are complexifications of known ones. In particular, we find that the general left-invariant metric on S3 and the metric 'Sol' admit no local solutions of the Einstein–Weyl equations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1006621831435
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