On a conjecture of J. M. Lee
type: Item
instance of: scholarly article
title: On a conjecture of J. M. Lee
zbMATH Open document ID: 0797.53036
author: Sorin Dragomir
published in: Hokkaido Mathematical Journal
publication date: 1994-10-18T00:00:00Z
review text: The following conjecture of J. M. Lee is discussed: compact strictly pseudo-convex \(CR\) manifolds whose \(CR\) structure has a vanishing first Chern class admit a global pseudo-Einstein structure. Using the parabolic dilations of the Heisenberg group the author constructs a family \(H_ n(s)\), \(0 < s < 1\) of compact strictly pseudo-convex \(CR\) manifolds, so that each \(H_ n(s)\) satisfies the Lee conjecture. Endowing \(H_ n(s)\) with a contact form \(\theta\) he proves: Theorem 2. Let \(0 < s < 1\) and \(n > 1\). Then i) all Chern classes of \({\mathcal H}_ s = T_{1,0}(H_ n(s))\) vanish, and ii) the contact form \(\theta\) is pseudo-Einstein and has non-vanishing pseudo-Hermitian torsion. Also the Lee conjecture for compact strictly pseudo-convex \(CR\) manifolds with a regular contact vector is solved affirmatively.
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 569378
zbMATH Keywords: \(CR\) manifolds
zbMATH Keywords: first Chern class
zbMATH Keywords: pseudo-Einstein structure
zbMATH Keywords: contact form
Wikidata QID: Q123001128
reviewed by: Grozio Stanilov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381412484
OpenAlex ID: W1999007129
DOI: 10.14492/HOKMJ/1381412484
description: scientific article; zbMATH DE number 569378