Standard Tractors and the Conformal Ambient Metric Construction

By Andreas Čap, A. Gover. 2002

130 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/66a5275c9defd2320b04d4b7faab2972cc120054

How researchers see this paper

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In Applied Mathematics

1. Andreas Čap
2. A. Gover
3. Michael Eastwood
4. Jeffrey S. Case
5. Sun‐Yung Alice Chang

In Astronomy and Astrophysics

1. Andreas Čap
2. A. Gover
3. Sun‐Yung Alice Chang
4. Jeffrey S. Case

In Nuclear and High Energy Physics

1. Andreas Čap
2. A. Gover

Citations in the corpus

• CR-Tractors and the Fefferman Space (2006, background): “is a density bundle on M̃ , which (in the conventions of [9] but using a tilde”