Conformal transformation groups of Lorentzian manifolds

by Prof. Karin Melnick

Tuesday 2 Jul 2024, 05:00 → 06:00 Europe/Berlin

H4 (Geom)

Abstract:

By the celebrated theorem of Ferrand and Obata from 1971, the conformal group of a closed Riemannian manifold M is compact, 
unless M is conformally equivalent to the round sphere.  For pseudo-Riemannian manifolds, the analogous statement is false, by 
counterexamples due to C. Frances.  For Lorentzian manifolds of dimension at least 3, however, it is conjectured that whenever the 
conformal group does not preserve any metric in the conformal class---in which case it is called essential---then the manifold is locally c
onformally flat.  I will discuss recent work toward resolving this conjecture and toward classifying the groups G and the closed Lorentzian 
manifolds M such that G is an essential conformal group for M.