The projective Lichnerowicz–Obata conjecture

Let $(M^n,g)$ be a complete connected or closed connected semi-Riemannian manifold, and let $G$ be a connected Lie group acting on $M$ by projective transformations.

Projective Lichnerowicz–Obata conjecture. Either $G$ acts on $M$ by affine transformations, or $(M^n,g)$ is Riemannian with positive constant sectional curvature.

This conjecture is a global rigidity statement for projective transformation groups of semi-Riemannian manifolds. The supplied source does not indicate whether it has been resolved.