Canonical contact forms on spherical CR manifolds

Wang, 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 -