On a discretization of confocal quadrics. I. An integrable systems approach

dc.contributor.authorBobenko, Alexander I.
dc.contributor.authorSchief, Wolfgang K.
dc.contributor.authorSuris, Yuri B.
dc.contributor.authorTechter, Jan
dc.date.accessioned2021-04-15T08:44:19Z
dc.date.available2021-04-15T08:44:19Z
dc.date.issued2016-08-04
dc.description.abstractConfocal quadrics lie at the heart of the system of confocal coordinates (also called elliptic coordinates, after Jacobi). We suggest a discretization which respects two crucial properties of confocal coordinates: separability and all two-dimensional coordinate subnets being isothermic surfaces (that is, allowing a conformal parametrization along curvature lines, or, equivalently, supporting orthogonal Koenigs nets). Our construction is based on an integrable discretization of the Euler–Poisson–Darboux equation and leads to discrete nets with the separability property, with all two-dimensional subnets being Koenigs nets, and with an additional novel discrete analogue of the orthogonality property. The coordinate functions of our discrete nets are given explicitly in terms of gamma functions.en
dc.description.sponsorshipDFG, 195170736, TRR 109: Diskretisierung in Geometrie und Dynamiken
dc.identifier.eissn2058-5985
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/13030
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-11827
dc.language.isoenen
dc.relation.ispartof10.14279/depositonce-11461
dc.rights.urihttps://creativecommons.org/licenses/by-nc/4.0/en
dc.subject.ddc516 Geometriede
dc.subject.otherdiscrete integrable systemsen
dc.subject.otherdiscrete differential geometryen
dc.subject.otherdiscrete elliptic coordinatesen
dc.subject.otherKoenigs netsen
dc.subject.otherconfocal quadricsen
dc.titleOn a discretization of confocal quadrics. I. An integrable systems approachen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.articlenumberxyw005en
dcterms.bibliographicCitation.doi10.1093/integr/xyw005en
dcterms.bibliographicCitation.issue1en
dcterms.bibliographicCitation.journaltitleJournal of Integrable Systemsen
dcterms.bibliographicCitation.originalpublishernameOxford University Pressen
dcterms.bibliographicCitation.originalpublisherplaceOxforden
dcterms.bibliographicCitation.volume1en
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften>Inst. Mathematik>FG Geometrie und Visualisierungde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.groupFG Geometrie und Visualisierungde
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
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