On the geometry of closed G2-structure
| dc.creator | Cleyton, Richard | |
| dc.creator | Ivanov, Stefan | |
| dc.date | 2003-06-25 | |
| dc.date | 2005-03-14 | |
| dc.date.accessioned | 2026-07-07T11:32:27Z | |
| dc.date.available | 2026-07-07T11:32:27Z | |
| dc.description | We give an answer to a question posed recently by R.Bryant, namely we show that a compact 7-dimensional manifold equipped with a G2-structure with closed fundamental form is Einstein if and only if the Riemannian holonomy of the induced metric is contained in G2. This could be considered to be a G2 analogue of the Goldberg conjecture in almost Kahler geometry. The result was generalized by R.L.Bryant to closed G2-structures with too tightly pinched Ricci tensor. We extend it in another direction proving that a compact G2-manifold with closed fundamental form and divergence-free Weyl tensor is a G2-manifold with parallel fundamental form. We introduce a second symmetric Ricci-type tensor and show that Einstein conditions applied to the two Ricci tensors on a closed G2-structure again imply that the induced metric has holonomy group contained in G2. | |
| dc.description | 14 pages, the Einstein condition in the assumptions of the Main theorem is generalized to the assumption that the Weyl tensor is divergence-free, clarity improved, typos corrected | |
| dc.identifier | https://arxiv.org/abs/math/0306362 | |
| dc.identifier | http://arxiv.org/abs/math/0306362 | |
| dc.identifier | Commun.Math.Phys.270:53-67,2007 | |
| dc.identifier | doi:10.1007/s00220-006-0145-7 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/197600 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C10 (Primary); 53C25, 53C29 (Secondary) | |
| dc.title | On the geometry of closed G2-structure | |
| dc.type | text |