# Canonical contact forms on spherical CR manifolds

Journal of the European Mathematical Society (2003)

- Volume: 005, Issue: 3, page 245-273
- ISSN: 1435-9855

## Access Full Article

top## Abstract

top## How to cite

topWang, Wei. "Canonical contact forms on spherical CR manifolds." Journal of the European Mathematical Society 005.3 (2003): 245-273. <http://eudml.org/doc/277795>.

@article{Wang2003,

abstract = {We construct the CR invariant canonical contact form $\operatorname\{can\}(J)$ 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 $\Omega (\Gamma )/\Gamma $, where $\Gamma $ is a convex cocompact subgroup of $\operatorname\{Aut\}_\{CR\}\text\{S\}^\{2n+1\}=PU(n+1,1)$ and $\Omega (\Gamma )$ is the discontinuity domain of $\Gamma $. This contact form can be used to prove that $\Omega (\Gamma )/\Gamma $ is scalar positive (respectively, scalar negative, or scalar vanishing) if and only if the critical exponent $\delta (\Gamma )<n$ (respectively, $\delta (\Gamma )<n$, or $\delta (\Gamma )=n$). This generalizes Nayatani’s result for convex cocompact subgroups of $SO(n+1,1)$. We also discuss the connected sum of spherical CR manifolds.},

author = {Wang, Wei},

journal = {Journal of the European Mathematical Society},

keywords = {spherical CR manifolds; contact forms; connection; conformal sub-Laplacian; Webster scalar curvature; spherical CR manifolds; contact forms; connection; conformal sub-Laplacian; Webster scalar curvature},

language = {eng},

number = {3},

pages = {245-273},

publisher = {European Mathematical Society Publishing House},

title = {Canonical contact forms on spherical CR manifolds},

url = {http://eudml.org/doc/277795},

volume = {005},

year = {2003},

}

TY - JOUR

AU - Wang, Wei

TI - Canonical contact forms on spherical CR manifolds

JO - Journal of the European Mathematical Society

PY - 2003

PB - European Mathematical Society Publishing House

VL - 005

IS - 3

SP - 245

EP - 273

AB - We construct the CR invariant canonical contact form $\operatorname{can}(J)$ 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 $\Omega (\Gamma )/\Gamma $, where $\Gamma $ is a convex cocompact subgroup of $\operatorname{Aut}_{CR}\text{S}^{2n+1}=PU(n+1,1)$ and $\Omega (\Gamma )$ is the discontinuity domain of $\Gamma $. This contact form can be used to prove that $\Omega (\Gamma )/\Gamma $ is scalar positive (respectively, scalar negative, or scalar vanishing) if and only if the critical exponent $\delta (\Gamma )<n$ (respectively, $\delta (\Gamma )<n$, or $\delta (\Gamma )=n$). This generalizes Nayatani’s result for convex cocompact subgroups of $SO(n+1,1)$. We also discuss the connected sum of spherical CR manifolds.

LA - eng

KW - spherical CR manifolds; contact forms; connection; conformal sub-Laplacian; Webster scalar curvature; spherical CR manifolds; contact forms; connection; conformal sub-Laplacian; Webster scalar curvature

UR - http://eudml.org/doc/277795

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.