A remark on minimal foliations of Lie groups
type: Item
instance of: scholarly article
title: A remark on minimal foliations of Lie groups
zbMATH Open document ID: 0585.53052
author: Shin-ichi Nagamine
published in: Tsukuba Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: Let G be a 3-dimensional, simply connected nonunimodular Lie group with left invariant metric. If the foliation given by a 1- or 2-dimensional subalgebra of left invariant vector fields is minimal with bundle like metric, then G is isomorphic to a semi-direct product \(S\times {\mathbb{R}}\). Here S is the group of upper triangular matrices in SL(2,\({\mathbb{R}})\), and inherits a metric of constant negative curvature.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 22E15
zbMATH DE Number: 3938008
zbMATH Keywords: minimal foliation
zbMATH Keywords: nonunimodular Lie group
zbMATH Keywords: bundle like metric
Wikidata QID: Q115233625
reviewed by: Dirk Ferus
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496160293
OpenAlex ID: W1495939361
DOI: 10.21099/TKBJM/1496160293
Recommended article: Minimal foliations on Lie groups
Recommended article: Q4656894
Recommended article: Some remarks on minimal foliations
Recommended article: Conformal minimal foliations on semi-Riemannian Lie groups
Recommended article: A remark on minimal foliations of codimension two
Recommended article: Foliations by planes and Lie group actions
Recommended article: A class of totally geodesic foliations of Lie groups
Recommended article: The diffeomorphism group of a Lie foliation
Recommended article: Q3182044
description: scientific article; zbMATH DE number 3938008