On conformally invariant differential operators

Details On conformally invariant differential operators On conformally invariant differential operators

2006-08-31

arxiv.org/abs/math/0608771v3

Mathematics

Differential Geometry

50 pages, revised version

Scientific paper

We construct new families of conformally invariant differential operators acting on densities. We introduce a simple, direct approach which shows that all such operators arise via this construction when the degree is bounded by the dimension. The method relies on a study of well-known transformation laws and on Weyl's theory regarding identities holding ``formally'' vs. ``by substitution''. We also illustrate how this new method can strengthen existing results in the parabolic invariant theory for conformal geometries.

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