Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 22 (2026), 061, 26 pages      arXiv:2505.14665      https://doi.org/10.3842/SIGMA.2026.061

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

Karin Melnick a and Katharina Neusser b
a) Department of Mathematics, University of Luxembourg, 6 avenue de la Fonte, L-4364 Esch-sur-Alzette, Luxembourg
b) Department of Mathematics and Statistics, Masaryk University, Kotlav rská 267/2, 611 37 Brno, Czech Republic

Received October 14, 2025, in final form June 04, 2026; Published online June 22, 2026

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.

Key words: Cartan geometries; parabolic geometries; conformal manifolds; automorphisms of geometric structures; pseudo-Riemannian geometry; simple Lie transformation groups.

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