# The Lorentzian Lichnerowicz Conjecture for real-analytic, three-dimensional manifolds

@inproceedings{Frances2021TheLL, title={The Lorentzian Lichnerowicz Conjecture for real-analytic, three-dimensional manifolds}, author={Charles Frances and Karin Melnick}, year={2021} }

The Lichnerowicz Conjecture in conformal Riemannian geometry was proved simultaneously by J. Ferrand and M. Obata. Recall that the conformal transformations of a semi-Riemannian manifold (M, g) form the group Conf(M, [g]) = {f ∈ Diff(M) : f∗g = eg, λ ∈ C∞(M)} and that this is a Lie group provided dim M ≥ 3. A subgroup H ≤ Conf(M, [g]) is called essential if it does not act isometrically with respect any g′ = e2λg in the conformal class [g] of g. The identity component of a Lie group H is…

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