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Conformal transformation groups of Lorentzian manifolds

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TWT - Twistor theory

By the celebrated theorem of Ferrand and Obata from 1971, the conformalgroup of a closed Riemannian manifold M is compact, unless M is conformally equivalentto the round sphere. For pseudo-Riemannian manifolds, the analogous statementis false, by counterexamples due to C. Frances. For Lorentzian manifolds of dimensionat least 3, however, it is conjectured that whenever the conformal group does not preserveany metric in the conformal class—in which case it is called essential—then themanifold is locally conformally flat. I will discuss recent work toward resolving thisconjecture and toward classifying the groups G and the closed Lorentzian manifoldsM such that G is an essential conformal group for M.

This talk is part of the Isaac Newton Institute Seminar Series series.

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