An Embedding Theorem for Tractor Bundles, and an Application in Conformal Pseudo-Riemannian Geometry

Abstract

We provide an extension of the Gromov-Zimmer embedding theorem for Cartan geometries of [Bader U., Frances C., Melnick K., Geom. Funct. Anal. 19 (2009), 333-355, arXiv:0709.3844] to tractor bundles carrying any invariant connection, including tractor connections and prolongation connections of first BGG operators for parabolic geometries. As an application, we prove a rigidity result for conformal actions of special pseudo-unitary groups on closed, simply connected, analytic pseudo-Riemannian manifolds.