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math.DG2026
A local Lorentzian Ferrand-Obata theorem for conformal vector fields
Sorin Dumitrescu, Charles Frances, Karin Melnick +2
For a conformal vector field on a closed, real-analytic, Lorentzian manifold we prove that the flow is locally isometric -- that it preserves a metric in the conformal class on a n…
math.DG2026
An Embedding Theorem for Tractor Bundles, and an Application in Conformal Pseudo-Riemannian Geometry
Karin Melnick, Katharina Neusser
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] t…
math.DG2024
Classification of closed conformally flat Lorentzian manifolds with unipotent holonomy
Rachel Lee, Karin Melnick
We classify closed, conformally flat Lorentzian manifolds of dimension with unipotent holonomy in PO(2,n). They are all Kleinian and fall into four different geometric t…