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Canonical contact forms on spherical CR manifolds

Authors
  • Wang, Wei1, 2
  • 1 Zhejiang University (Xixi campus), Department of Mathematics, Zhejiang, 310028, P.R. China , Zhejiang
  • 2 University of Toronto, Department of Mathematics, Ontario, M5S 3G3, Canada , Ontario
Type
Published Article
Journal
Journal of the European Mathematical Society
Publisher
Springer-Verlag
Publication Date
Mar 03, 2003
Volume
5
Issue
3
Pages
245–273
Identifiers
DOI: 10.1007/s10097-003-0050-8
Source
Springer Nature
Keywords
License
Yellow

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 AutCRS2n+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.

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