Conformal actions of nilpotent groups on pseudo-Riemannian manifolds
arXiv:0807.4735 · doi:10.1215/00127094-2010-030
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 nilpotent 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, conformally flat space, up to finite covers. The proofs make use of the canonical Cartan geometry associated to a pseudo-Riemannian conformal structure.
41 pages, 3 figures. Article has been shortened from previous version, and several corrections have been made according to referees' suggestions