An Embedding Theorem for tractor bundles, and an application in conformal pseudo-Riemannian geometry

2025/05/20 by Melnick, Karin, Neusser, Katharina · 1 citation
#53C50 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.14665

Abstract

We provide an extension of the Gromov--Zimmer Embedding Theorem for Cartan geometries of [3] 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.

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Cited by

• A local Lorentzian Ferrand-Obata theorem for conformal vector fields

Related

• Subtleties Concerning Conformal Tractor Bundles
• Bundles of Weyl structures and invariant calculus for parabolic geometries
• Rigidity at the boundary for conformal structures and other Cartan geometries
• Projective Geometry I: Principles and Properties
• Homogeneous Cartan Geometries