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Almost conformally Einstein manifolds and obstructions

A. R. Gover
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Abstract

A Riemannian or pseudo-Riemannian (or conformal) structure is conformally Einstein if and only if there is a suitably generic parallel section of a certain vector bundle -- the so-called standard conformal tractor bundle. We show that this characterisation leads to a systematic approach to constructing obstructions to conformally Einstein metrics. Relaxing the requirement that the parallel tractor field be generic gives a natural generalisation of the Einstein equations.

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A. R. Gover. 2004-12-20. Almost conformally Einstein manifolds and obstructions. https://arxiv.org/abs/math/0412393

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