Higher order parallel surfaces in three-dimensional homogeneous spaces
| dc.creator | Van der Veken, Joeri | |
| dc.date | 2006-04-25 | |
| dc.date | 2008-02-08 | |
| dc.date.accessioned | 2026-07-07T09:19:21Z | |
| dc.date.available | 2026-07-07T09:19:21Z | |
| dc.description | We give a full classification of higher order parallel surfaces in three-dimensional homogeneous spaces with four-dimensional isometry group, i.e. in the so-called Bianchi-Cartan-Vranceanu family. This gives a positive answer to a conjecture formulated in 2002. As a partial result, we prove that totally umbilical surfaces only exist if the space is a Riemannian product of a surface of constant Gaussian curvature and the real line, and we give a local parametrization of all totally umbilical surfaces. | |
| dc.description | To appear under the title "Higher order parallel surfaces in Bianchi-Cartan-Vranceanu spaces" in Result. Math. (in press) | |
| dc.identifier | https://arxiv.org/abs/math/0604541 | |
| dc.identifier | http://arxiv.org/abs/math/0604541 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154359 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53B25 (Primary), 53C40 (Secondary) | |
| dc.title | Higher order parallel surfaces in three-dimensional homogeneous spaces | |
| dc.type | text |