CR-tractors and the Fefferman space

Parabolic Geometries, CR–Tractors, and the Fefferman Construction

This is a survey on recent joint work with A.R. Gover on the geometry of non–degenerate CR manifolds of hypersurface type. Specifically we discuss the relation between standard tractors on one side and the canonical Cartan connection, the construction of the Fefferman space and the ambient metric construction on the other side. To put these results into perspective, some parts of the general th...

Parabolic Geometries , Cr { Tractors , And

Diffeomorphisms, Anomalies and the Fefferman-Graham Ambiguity ∗

Using the Weyl transfomations induced by diffeomorphisms we set up a cohomological problem for the Fefferman-Graham coefficients. The cohomologically nontrivial solutions remove the ambiguity and give the nonlocal terms in the effective action responsible for the trace anomalies.

Some Remarks on the Fefferman-stein Inequality

We investigate the Fefferman-Stein inequality related a function f and the sharp maximal function f on a Banach function space X. It is proved that this inequality is equivalent to a certain boundedness property of the Hardy-Littlewood maximal operatorM . The latter property is shown to be self-improving. We apply our results in several directions. First, we show the existence of nontrivial spa...

An Analog of the Fefferman Construction

The Fefferman construction associates to a manifold carrying a CR–structure a conformal structure on a sphere bundle over the manifold. There are some analogs to this construction, with one giving a Lie contact structure, a refinement of the contact bundle on the bundle of rays in the cotangent bundle of a manifold with a conformal metric. Since these structures are parabolic geometries, these ...