Lorentzian Lichnerowicz conjecture

Let $M$ be a closed Lorentzian conformal manifold. It is essential if its conformal transformation group does not preserve any metric in the conformal class. Lorentzian Lichnerowicz conjecture. If $M$ is an essential, closed, Lorentzian conformal manifold, then $M$ is conformally flat.

The conjecture is a Lorentzian analogue of Lichnerowicz-type results concerning essential transformation groups of geometric structures. Significant progress is known, but the conjecture remains unresolved in full generality.