As is well-known, the real rank of a simple Lie group that acts conformally on a pseudo-Riemannian manifold is bounded by means of the signature of the manifold. We give a precise description of the action whenever the real rank of the group reaches that bound, assuming the action is minimal.
"Conformal Actions of Simple Lie Groups on Compact Pseudo-Riemannian Manifolds." J. Differential Geom. 60 (3) 355 - 387, March, 2002. https://doi.org/10.4310/jdg/1090351122