Projective transformation groups of pseudo-Riemannian manifolds
Abdelghani Zeghib

To a pseudo-Riemannian metric (M, g) is naturally associated many transformation groups, namely: Isom(M, g), its isometry group,  Conf(M, g) its conformal group,  Affin(M, g)  its affine group consisting of those transformations preserving the Levi-Cevita connection of g or equivalently its (parameterized) geodesics, and finally Proj(M, g) its group of projective transformations which preserve unparameterized geodesics. Obvious inclusions are satisfied between these groups. It turns out however that, except in very special cases,  all these inclusions are trivial, that is all these groups are equal to Isom(M, g). We are interested here in the case where Proj(M, g) contains properly Affin(M, g)?