Inhomogeneous Ambient Metrics

Details Inhomogeneous Ambient Metrics Inhomogeneous Ambient Metrics

2006-11-30

arxiv.org/abs/math/0611931v1

Mathematics

Differential Geometry

18 pages

Scientific paper

An extension of the ambient metric construction of Fefferman-Graham to infinite order in even dimensions is described. The main ingredients are the introduction of "inhomogeneous ambient metrics" with asymptotic expansions involving the logarithm of a defining function homogeneous of degree 2, and an invariant procedure for taking the smooth part of such an inhomogeneous ambient metric. The metrics which result depend on the choice of an "ambiguity tensor" as well as a conformal class. An application to the description of scalar conformal invariants in even dimensions is outlined.

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