Jacobi fields along harmonic 2-spheres in $S^3$ and $S^4$ are not all integrable
| dc.creator | Lemaire, Luc | |
| dc.creator | Wood, John C | |
| dc.date | 2007-09-10 | |
| dc.date | 2007-12-20 | |
| dc.date.accessioned | 2026-07-07T08:50:13Z | |
| dc.date.available | 2026-07-07T08:50:13Z | |
| dc.description | In a previous paper, we showed that any Jacobi field along a harmonic map from the 2-sphere to the complex projective plane is integrable (i.e., is tangent to a smooth variation through harmonic maps). In this paper, in contrast, we show that there are (non-full) harmonic maps from the 2-sphere to the 3-sphere and 4-sphere which have non-integrable Jacobi fields. This is particularly surprising in the case of the 3-sphere where the space of harmonic maps of any degree is a smooth manifold, each map having image in a totally geodesic 2-sphere. | |
| dc.description | 43 pages. Some typos corrected; introduction expanded | |
| dc.identifier | https://arxiv.org/abs/0709.1417 | |
| dc.identifier | http://arxiv.org/abs/0709.1417 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144532 | |
| dc.subject | Differential Geometry | |
| dc.subject | 58E20; 53C43 | |
| dc.title | Jacobi fields along harmonic 2-spheres in $S^3$ and $S^4$ are not all integrable | |
| dc.type | text |