Duke Mathematical Journal

Conformal actions of nilpotent groups on pseudo-Riemannian manifolds

Charles Frances and Karin Melnick

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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 pq; 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

Article information

Duke Math. J., Volume 153, Number 3 (2010), 511-550.

First available in Project Euclid: 4 June 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53A30: Conformal differential geometry
Secondary: 53C50: Lorentz manifolds, manifolds with indefinite metrics


Frances, Charles; Melnick, Karin. Conformal actions of nilpotent groups on pseudo-Riemannian manifolds. Duke Math. J. 153 (2010), no. 3, 511--550. doi:10.1215/00127094-2010-030. https://projecteuclid.org/euclid.dmj/1275671396

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