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Detecting Einstein geodesics: Einstein metrics in projective and conformal geometry

Gover, Rod; Macbeth, H R M


Here we treat the problem: given a torsion-free connection do its geodesics, as unparametrised curves, coincide with the geodesics of an Einstein metric? We find projective invariants such that the vanishing of these is necessary for the existence of such a metric, and in generic settings the vanishing of these is also sufficient. We also obtain results for the problem of metrisability (without the Einstein condition): We show that the odd Chern type invariants of an affine connection are...[Show more]

CollectionsANU Research Publications
Date published: 2014
Type: Journal article
Source: Differential Geometry and its Applications
DOI: 10.1016/j.difgeo.2013.10.011


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