Biharmonic maps and morphisms from conformal mappings
| dc.creator | Loubeau, E. | |
| dc.creator | Ou, Y. -L. | |
| dc.date | 2008-04-10 | |
| dc.date.accessioned | 2026-07-07T09:31:36Z | |
| dc.date.available | 2026-07-07T09:31:36Z | |
| dc.description | Inspired by the all-important conformal invariance of harmonic maps on two-dimensional domains, this article studies the relationship between biharmonicity and conformality. We first give a characterization of biharmonic morphisms, analogues of harmonic morphisms investigated by Fuglede and Ishihara, which, in particular, explicits the conditions required for a conformal map in dimension four to preserve biharmonicity and helps producing the first example of a biharmonic morphism which is not a special type of harmonic morphism. Then, we compute the bitension field of horizontally weakly conformal maps, which include conformal mappings. This leads to several examples of proper (i.e. non-harmonic) biharmonic conformal maps, in which dimension four plays a pivotal role. We also construct a family of Riemannian submersions which are proper biharmonic maps. | |
| dc.identifier | https://arxiv.org/abs/0804.1752 | |
| dc.identifier | http://arxiv.org/abs/0804.1752 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158516 | |
| dc.subject | Differential Geometry | |
| dc.subject | 58E20 | |
| dc.title | Biharmonic maps and morphisms from conformal mappings | |
| dc.type | text |