Projective transformation groups of pseudo-Riemannian manifolds
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)?