Jet isomorphism for conformal geometry

TL;DR

This paper discusses jet isomorphism theorems in conformal geometry, providing new proofs and formulations for both odd and even dimensions using ambient metric techniques and deformation complexes.

Contribution

It introduces novel proofs and formulations of jet isomorphism theorems in conformal geometry, including an ambient realization and inhomogeneous ambient metrics.

Findings

New proof of jet isomorphism theorem for odd-dimensional conformal geometry

Formulation of jet isomorphism theorem for even-dimensional conformal geometry

Description of an infinite order ambient lift for conformal densities

Abstract

Jet isomorphism theorems for conformal geometry are discussed. A new proof of the jet isomorphism theorem for odd-dimensional conformal geometry is outlined, using an ambient realization of the conformal deformation complex. An infinite order ambient lift for conformal densities in the case in which harmonic extension is obstructed is described. A jet isomorphism theorem for even dimensional conformal geometry is formulated using the inhomogeneous ambient metrics recently introduced by the author and K. Hirachi.