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Canonical contact forms on spherical CR manifolds

Canonical contact forms on spherical CR manifolds We construct the CR invariant canonical contact form can(J) on scalar positive spherical CR manifold (M,J), which is the CR analogue of canonical metric on locally conformally flat manifold constructed by Habermann and Jost. We also construct another canonical contact form on the Kleinian manifold Ω(Γ)/Γ, where Γ is a convex cocompact subgroup of Aut CR S 2n+1=PU(n+1,1) and Ω(Γ) is the discontinuity domain of Γ. This contact form can be used to prove that Ω(Γ)/Γ is scalar positive (respectively, scalar negative, or scalar vanishing) if and only if the critical exponent δ(Γ)<n (respectively, δ(Γ)>n, or δ(Γ)=n). This generalizes Nayatani’s result for convex cocompact subgroups of SO(n+1,1). We also discuss the connected sum of spherical CR manifolds. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the European Mathematical Society Springer Journals

Canonical contact forms on spherical CR manifolds

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Publisher
Springer Journals
Copyright
Copyright © 2003 by Springer-Verlag
Subject
Mathematics
ISSN
1435-9855
eISSN
1435-9863
DOI
10.1007/s10097-003-0050-8
Publisher site
See Article on Publisher Site

Abstract

We construct the CR invariant canonical contact form can(J) on scalar positive spherical CR manifold (M,J), which is the CR analogue of canonical metric on locally conformally flat manifold constructed by Habermann and Jost. We also construct another canonical contact form on the Kleinian manifold Ω(Γ)/Γ, where Γ is a convex cocompact subgroup of Aut CR S 2n+1=PU(n+1,1) and Ω(Γ) is the discontinuity domain of Γ. This contact form can be used to prove that Ω(Γ)/Γ is scalar positive (respectively, scalar negative, or scalar vanishing) if and only if the critical exponent δ(Γ)<n (respectively, δ(Γ)>n, or δ(Γ)=n). This generalizes Nayatani’s result for convex cocompact subgroups of SO(n+1,1). We also discuss the connected sum of spherical CR manifolds.

Journal

Journal of the European Mathematical SocietySpringer Journals

Published: Mar 3, 2003

References