  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.

Differential Geometry