Conformal actions of nilpotent groups on pseudo-Riemannian manifolds

Abstract. We study conformal actions of connected nilpotent Lie groups on compact pseudo-Riemannian manifolds. We prove that if a type-(p, q) compact manifold M supports a conformal action of a connected nilpo-tent group H, then the degree of nilpotence of H is at most 2p + 1, assuming p ≤ q; further, if this maximal degree is attained, then M is conformally equivalent to the universal type-(p, q), compact, confor-mally flat space, up to finite or cyclic covers. The proofs make use of the canonical Cartan geometry associated to a pseudo-Riemannian conformal structure. 1