Conformal equivalence between certain geometries in dimension 6 and 7
| dc.creator | Cleyton, Richard | |
| dc.creator | Ivanov, Stefan | |
| dc.date | 2006-07-20 | |
| dc.date | 2006-07-26 | |
| dc.date.accessioned | 2026-07-07T07:20:43Z | |
| dc.date.available | 2026-07-07T07:20:43Z | |
| dc.description | For G_2-manifolds the Fernández-Gray class X_1+X_4 is shown to consist of the union of the class X_4 of G_2-manifolds locally conformal to parallel G_2-structures and that of conformal transformations of nearly parallel or weak holonomy G_2-manifolds of type X_1. The analogous conclusion is obtained for Gray-Hervella class W_1+W_4 of real 6-dimensional almost Hermitian manifolds: this sort of geometry consists of locally conformally Kähler manifolds of class W_4 and conformal transformations of nearly Kähler manifolds in class W_1. A corollary of this is that a compact SU(3)-space in class W_1+W_4 or G_2-space of the kind X_1+X_4 has constant scalar curvature if only if it is either a standard sphere or a nearly parallel G_2 or nearly Kähler manifold, respectively. The properties of the Riemannian curvature of the spaces under consideration are also explored. | |
| dc.description | 8 pages, typos and a sign inconsistency has been fixed | |
| dc.identifier | https://arxiv.org/abs/math/0607487 | |
| dc.identifier | http://arxiv.org/abs/math/0607487 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115048 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C25; 53C26; 53C15 | |
| dc.title | Conformal equivalence between certain geometries in dimension 6 and 7 | |
| dc.type | text |