Abstract
In this paper we relate the Fefferman–Graham ambientmetric construction for conformal manifolds to the approach toconformal geometry via the canonical Cartan connection. We show thatfrom any ambient metric that satisfies a weakening of the usualnormalisation condition, one can construct the conformal standardtractor bundle and the normal standard tractor connection, which areequivalent to the Cartan bundle and the Cartan connection. This resultis applied to obtain a procedure to get tractor formulae for allconformal invariants that can be obtained from the ambient metricconstruction. We also get information on ambient metrics whichare Ricci flat to higher order than guaranteed by the results ofFefferman–Graham.
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Čap, A., Gover, A.R. Standard Tractors and the Conformal Ambient Metric Construction. Annals of Global Analysis and Geometry 24, 231–259 (2003). https://doi.org/10.1023/A:1024726607595
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DOI: https://doi.org/10.1023/A:1024726607595