On a discretization of confocal quadrics. I. An integrable systems approach
| dc.contributor.author | Bobenko, Alexander I. | |
| dc.contributor.author | Schief, Wolfgang K. | |
| dc.contributor.author | Suris, Yuri B. | |
| dc.contributor.author | Techter, Jan | |
| dc.date.accessioned | 2021-04-15T08:44:19Z | |
| dc.date.available | 2021-04-15T08:44:19Z | |
| dc.date.issued | 2016-08-04 | |
| dc.description.abstract | Confocal 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.sponsorship | DFG, 195170736, TRR 109: Diskretisierung in Geometrie und Dynamik | en |
| dc.identifier.eissn | 2058-5985 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/13030 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-11827 | |
| dc.language.iso | en | en |
| dc.relation.ispartof | 10.14279/depositonce-11461 | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc/4.0/ | en |
| dc.subject.ddc | 516 Geometrie | de |
| dc.subject.other | discrete integrable systems | en |
| dc.subject.other | discrete differential geometry | en |
| dc.subject.other | discrete elliptic coordinates | en |
| dc.subject.other | Koenigs nets | en |
| dc.subject.other | confocal quadrics | en |
| dc.title | On a discretization of confocal quadrics. I. An integrable systems approach | en |
| dc.type | Article | en |
| dc.type.version | publishedVersion | en |
| dcterms.bibliographicCitation.articlenumber | xyw005 | en |
| dcterms.bibliographicCitation.doi | 10.1093/integr/xyw005 | en |
| dcterms.bibliographicCitation.issue | 1 | en |
| dcterms.bibliographicCitation.journaltitle | Journal of Integrable Systems | en |
| dcterms.bibliographicCitation.originalpublishername | Oxford University Press | en |
| dcterms.bibliographicCitation.originalpublisherplace | Oxford | en |
| dcterms.bibliographicCitation.volume | 1 | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Geometrie und Visualisierung | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.group | FG Geometrie und Visualisierung | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |