Conformal actions of nilpotent groups on pseudo-Riemannian manifolds

Details Conformal actions of nilpotent groups on pseudo-Riemannian manifolds Conformal actions of nilpotent groups on pseudo-Riemannian manifolds

2008-07-29

arxiv.org/abs/0807.4735v2

Duke Mathematical Journal, vol. 153, no. 3 (2010) pp 511-550

Mathematics

Differential Geometry

41 pages, 3 figures. Article has been shortened from previous version, and several corrections have been made according to ref

Scientific paper

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.

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