Nearly Kaehler and nearly parallel G_2-structures on spheres
| dc.creator | Friedrich, Thomas | |
| dc.date | 2005-09-07 | |
| dc.date.accessioned | 2026-07-07T05:23:00Z | |
| dc.date.available | 2026-07-07T05:23:00Z | |
| dc.description | In some other context, the question was raised how many nearly Kähler structures exist on the sphere $§^6$ equipped with the standard Riemannian metric. In this short note, we prove that, up to isometry, there exists only one. This is a consequence of the description of the eigenspace to the eigenvalue $λ= 12$ of the Laplacian acting on 2-forms. A similar result concerning nearly parallel $\G_2$-structures on the round sphere $§^7$ holds, too. An alternative proof by Riemannian Killing spinors is also indicated. | |
| dc.description | 2 pages, Latex2e | |
| dc.identifier | https://arxiv.org/abs/math/0509146 | |
| dc.identifier | http://arxiv.org/abs/math/0509146 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76276 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C25; 81T30 | |
| dc.title | Nearly Kaehler and nearly parallel G_2-structures on spheres | |
| dc.type | text |