Left-invariant hypercontact structures on three-dimensional Lie groups
type: Item
instance of: scholarly article
title: Left-invariant hypercontact structures on three-dimensional Lie groups
zbMATH Open document ID: 1340.53056
author: Giovanni Calvaruso
author: Antonella Perrone
published in: Periodica Mathematica Hungarica
publication date: 2015-01-07T00:00:00Z
review text: The authors prove that a 3-manifold \(M\) is parallelizable if and only if one of the following assertions holds: {\parindent=0.6cm\begin{itemize}\item[(i)] \(M\) admits an almost contact metric 3-structure; \item[(ii)] \(M\) admits a mixed metric 3-structure. \end{itemize}} As a consequence, they show that a three-dimensional Lie groups \(G\) admits a left-invariant hypercontact metric structure if and only if the universal covering \(\tilde{G}\) is \(\mathrm{SU}(2)\) or \(\tilde{\mathrm{SL}}(2,{\mathbf R})\).
reviewed by: Gabriel Teodor Pripoae
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53B05
Mathematics Subject Classification ID: 53D15
Mathematics Subject Classification ID: 22E99
zbMATH DE Number: 6384179
zbMATH Keywords: parallelizable 3-manifold
zbMATH Keywords: left-invariant hypercontact structure
zbMATH Keywords: three-dimensional Lie group
zbMATH Keywords: almost contact metric 3-structure
zbMATH Keywords: mixed metric 3-structure
zbMATH Keywords: taut contact sphere
Wikidata QID: Q115381954
MaRDI profile type: Publication
full work available at URL: s10998-014-0054-z
OpenAlex ID: W2093271751
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DOI: 10.1007/S10998-014-0054-Z
description: scientific article; zbMATH DE number 6384179