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Standard tractors and the conformal ambient metric construction (2003)
| Venue: | ANN. GLOBAL ANAL. GEOM |
| Citations: | 57 - 20 self |
BibTeX
@ARTICLE{Čap03standardtractors,
author = {Andreas Čap and A. Rod Gover},
title = {Standard tractors and the conformal ambient metric construction},
journal = {ANN. GLOBAL ANAL. GEOM},
year = {2003},
volume = {24},
pages = {231--259}
}
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Abstract
In this paper we relate the Fefferman–Graham ambient metric construction for conformal manifolds to the approach to conformal geometry via the canonical Cartan connection. We show that from any ambient metric that satisfies a weakening of the usual normalisation condition, one can construct the conformal standard tractor bundle and the normal standard tractor connection, which are equivalent to the Cartan bundle and the Cartan connection. This result is applied to obtain a procedure to get tractor formulae for all conformal invariants that can be obtained from the ambient metric construction. We also get information on ambient metrics which are Ricci flat to higher order than guaranteed by the results of Fefferman–Graham.
Keyphrases
standard tractor conformal ambient metric construction ambient metric construction conformal manifold cartan connection normal standard tractor connection fefferman graham ambient metric construction tractor formula ambient metric conformal invariant conformal geometry conformal standard tractor bundle cartan bundle usual normalisation condition fefferman graham canonical cartan connection
