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dc.contributor.authorFässler, Katrin
dc.contributor.authorLe Donne, Enrico
dc.date.accessioned2020-05-19T10:31:41Z
dc.date.available2020-05-19T10:31:41Z
dc.date.issued2020
dc.identifier.citationFässler, Katrin; Le Donne, Enrico (2020). On the quasi-isometric and bi-Lipschitz classification of 3D Riemannian Lie groups. Geometriae Dedicata, Early online. DOI: 10.1007/s10711-020-00532-8
dc.identifier.otherCONVID_35662662
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/69065
dc.description.abstractThis note is concerned with the geometric classification of connected Lie groups of dimension three or less, endowed with left-invariant Riemannian metrics. On the one hand, assembling results from the literature, we give a review of the complete classification of such groups up to quasi-isometries and we compare the quasi-isometric classification with the bi-Lipschitz classification. On the other hand, we study the problem whether two quasi-isometrically equivalent Lie groups may be made isometric if equipped with suitable left-invariant Riemannian metrics. We show that this is the case for three-dimensional simply connected groups, but it is not true in general for multiply connected groups. The counterexample also demonstrates that ‘may be made isometric’ is not a transitive relation.en
dc.format.mimetypeapplication/pdf
dc.languageeng
dc.publisherSpringer
dc.relation.ispartofseriesGeometriae Dedicata
dc.rightsCC BY 4.0
dc.subject.otherLie groups
dc.subject.otherquasi-isometric
dc.subject.otherbi-Lipschitz
dc.subject.otherisometric
dc.subject.otherRiemannian manifold
dc.subject.otherclassification
dc.titleOn the quasi-isometric and bi-Lipschitz classification of 3D Riemannian Lie groups
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202005193319
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.description.reviewstatuspeerReviewed
dc.relation.issn0046-5755
dc.relation.volumeEarly online
dc.type.versionpublishedVersion
dc.rights.copyright© The Authors, 2020
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber713998
dc.relation.grantnumber713998
dc.relation.grantnumber288501
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/713998/EU//GeoMeG
dc.subject.ysodifferentiaaligeometria
dc.subject.ysogeometria
dc.subject.ysoryhmäteoria
dc.subject.ysometriset avaruudet
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p16682
jyx.subject.urihttp://www.yso.fi/onto/yso/p8708
jyx.subject.urihttp://www.yso.fi/onto/yso/p12497
jyx.subject.urihttp://www.yso.fi/onto/yso/p27753
dc.rights.urlhttps://creativecommons.org/licenses/by/4.0/
dc.relation.doi10.1007/s10711-020-00532-8
dc.relation.funderEuroopan komissiofi
dc.relation.funderSuomen Akatemiafi
dc.relation.funderEuropean Commissionen
dc.relation.funderAcademy of Finlanden
jyx.fundingprogramERC Starting Grantfi
jyx.fundingprogramAkatemiatutkijan tehtävä, SAfi
jyx.fundingprogramERC Starting Granten
jyx.fundingprogramResearch post as Academy Research Fellow, AoFen
jyx.fundinginformationKatrin Fässler was partially supported by the Academy of Finland (Grant 285159 ‘Sub-Riemannian manifolds from a quasiconformal viewpoint’) and by the Swiss National Science Foundation (Grant 161299 ‘Intrinsic rectifiability and mapping theory on the Heisenberg group’). Enrico Le Donne was partially supported by the Academy of Finland (Grant 288501 ‘Geometry of subRiemannian groups’) and by the European Research Council (ERC Starting Grant 713998 GeoMeG ‘Geometry of Metric Groups’).


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