2008/07/31 by Charles Frances, Karin Melnick
Mathematics · #Action (physics) #Conformal geometry #Conformal map #Degree (music) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Lie group #Manifold (fluid mechanics) #Nilpotent #Simply connected space #math.DG #math.DS
paper · pdf · doi:10.1215/00127094-2010-030
published as Duke Math. J. 153, no. 3 (2010), 511-550 · 41 pages, 3 figures. Article has been shortened from previous version, and several corrections have been made according to referees' suggestions
openalex publication_date 2010/06/04 · arxiv created 2010/06/23 · openalex created_date 2016/06/24 · arxiv updated 2019/12/19 · openalex updated_date 2026/08/05
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 or cyclic covers. The proofs make use of the canonical Cartan geometry associated to a pseudo-Riemannian conformal structure