Pseudo-conformal invariants of type (1,3) of CR manifolds
type: Item
instance of: scholarly article
title: Pseudo-conformal invariants of type (1,3) of CR manifolds
zbMATH Open document ID: 0727.53039
author: Shukichi Tanno
published in: Hokkaido Mathematical Journal
publication date: 1991-01-01T00:00:00Z
review text: Let (M,\(\eta\),g) be a real \((2n+1)\)-dimensional contact Riemannian manifold with a contact form \(\eta\) and a Riemannian metric g associated to \(\eta\). Denote by D the contact distribution on M and by \(D^*\) the dual of D. It is well known that D admits an almost complex structure J and thus M has a pseudo-Hermitian structure (\(\eta\),J). The author calls \(B\in \Gamma (D\otimes D^{*3})\) a pseudo-conformal invariant of type (1,3), if B of (M,\(\eta\),J) is the same with \(\bar B\) of (M,\(\eta\),J) for the change \(\eta\to {\bar \eta}=\sigma \eta\), where \(\sigma\) is a smooth function. The author proves that (M,\(\eta\),g) admits such an invariant which depends on the linear connection on M. In case the CR-structure associated with the contact Riemannian structure is integrable, this invariant is just the Chern-Moser invariant.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 32V05
zbMATH DE Number: 4201072
zbMATH Keywords: pseudoconformal invariant
zbMATH Keywords: contact Riemannian manifold
zbMATH Keywords: almost complex structure
zbMATH Keywords: pseudo-Hermitian structure
zbMATH Keywords: CR-structure
reviewed by: Aurel Bejancu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381413839
OpenAlex ID: W2051887120
DOI: 10.14492/HOKMJ/1381413839
description: scientific article; zbMATH DE number 4201072