dc.contributor.author | Fässler, Katrin | |
dc.contributor.author | Le Donne, Enrico | |
dc.date.accessioned | 2020-05-19T10:31:41Z | |
dc.date.available | 2020-05-19T10:31:41Z | |
dc.date.issued | 2021 | |
dc.identifier.citation | Fässler, K., & Le Donne, E. (2021). On the quasi-isometric and bi-Lipschitz classification of 3D Riemannian Lie groups. <i>Geometriae Dedicata</i>, <i>210</i>(1), 27-42. <a href="https://doi.org/10.1007/s10711-020-00532-8" target="_blank">https://doi.org/10.1007/s10711-020-00532-8</a> | |
dc.identifier.other | CONVID_35662662 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/69065 | |
dc.description.abstract | This 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.mimetype | application/pdf | |
dc.language | eng | |
dc.language.iso | eng | |
dc.publisher | Springer | |
dc.relation.ispartofseries | Geometriae Dedicata | |
dc.rights | CC BY 4.0 | |
dc.subject.other | Lie groups | |
dc.subject.other | quasi-isometric | |
dc.subject.other | bi-Lipschitz | |
dc.subject.other | isometric | |
dc.subject.other | Riemannian manifold | |
dc.subject.other | classification | |
dc.title | On the quasi-isometric and bi-Lipschitz classification of 3D Riemannian Lie groups | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-202005193319 | |
dc.contributor.laitos | Matematiikan ja tilastotieteen laitos | fi |
dc.contributor.laitos | Department of Mathematics and Statistics | en |
dc.contributor.oppiaine | Analyysin ja dynamiikan tutkimuksen huippuyksikkö | fi |
dc.contributor.oppiaine | Geometrinen analyysi ja matemaattinen fysiikka | fi |
dc.contributor.oppiaine | Matematiikka | fi |
dc.contributor.oppiaine | Analysis and Dynamics Research (Centre of Excellence) | en |
dc.contributor.oppiaine | Geometric Analysis and Mathematical Physics | en |
dc.contributor.oppiaine | Mathematics | en |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | |
dc.type.coar | http://purl.org/coar/resource_type/c_2df8fbb1 | |
dc.description.reviewstatus | peerReviewed | |
dc.format.pagerange | 27-42 | |
dc.relation.issn | 0046-5755 | |
dc.relation.numberinseries | 1 | |
dc.relation.volume | 210 | |
dc.type.version | publishedVersion | |
dc.rights.copyright | © The Authors, 2020 | |
dc.rights.accesslevel | openAccess | fi |
dc.relation.grantnumber | 713998 | |
dc.relation.grantnumber | 713998 | |
dc.relation.grantnumber | 288501 | |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/H2020/713998/EU//GeoMeG | |
dc.subject.yso | differentiaaligeometria | |
dc.subject.yso | geometria | |
dc.subject.yso | ryhmäteoria | |
dc.subject.yso | metriset avaruudet | |
dc.format.content | fulltext | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p16682 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p8708 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p12497 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p27753 | |
dc.rights.url | https://creativecommons.org/licenses/by/4.0/ | |
dc.relation.doi | 10.1007/s10711-020-00532-8 | |
dc.relation.funder | European Commission | en |
dc.relation.funder | Research Council of Finland | en |
dc.relation.funder | Euroopan komissio | fi |
dc.relation.funder | Suomen Akatemia | fi |
jyx.fundingprogram | ERC Starting Grant | en |
jyx.fundingprogram | Academy Research Fellow, AoF | en |
jyx.fundingprogram | ERC Starting Grant | fi |
jyx.fundingprogram | Akatemiatutkija, SA | fi |
jyx.fundinginformation | Katrin 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’). | |
dc.type.okm | A1 | |