English

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

Differential Geometry 2025-10-14 v2

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.

Keywords

Cite

@article{arxiv.2505.14665,
  title  = {An Embedding Theorem for tractor bundles, and an application in conformal pseudo-Riemannian geometry},
  author = {Karin Melnick and Katharina Neusser},
  journal= {arXiv preprint arXiv:2505.14665},
  year   = {2025}
}

Comments

hypotheses of Theorem 1.2 improved to allow p=q; improvements to proof of proposition 4.12; changes to introduction; details added in some sections