Distinguished dimensions for special Riemannian geometries
| dc.creator | Nurowski, Pawel | |
| dc.date | 2006-01-02 | |
| dc.date | 2006-04-17 | |
| dc.date.accessioned | 2026-07-07T06:58:27Z | |
| dc.date.available | 2026-07-07T06:58:27Z | |
| dc.description | The paper is based on relations between a ternary symmetric form defining the SO(3) geometry in dimension five and Cartan's works on isoparametric hypersurfaces in spheres. As observed by Bryant such a ternary form exists only in dimensions n_k=3k+2, where k=1,2,4,8. In these dimensions it reduces the orthogonal group to the subgroups H_k\subset SO(n_k), with H_1=SO(3), H_2=SU(3), H_4=Sp(3) and H_8=F_4. This enables studies of special Riemannian geometries with structure groups H_k in dimensions n_k. The neccessary and sufficient conditions for the H_k geometries to admit the characteristic connection are given. As an illustration nontrivial examples of SU(3) geometries in dimension 8 admitting characteristic connection are provided. Among them there are examples having nonvanishing torsion and satisfying Einstein equations with respect to either the Levi-Civita or the characteristic connections. | |
| dc.description | Section 9 has been changed, so that the relation between the 6th tensor defining SU(2)xSU(2) geometry in dimension 8 and isoparametric hypersurfaces with 6 different principal curvatures is explicit. A 5-form reducing GL(14,R) to SP(3) is added to the Appendix B | |
| dc.identifier | https://arxiv.org/abs/math/0601020 | |
| dc.identifier | http://arxiv.org/abs/math/0601020 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107360 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53A40, 53B15, 53C10 | |
| dc.title | Distinguished dimensions for special Riemannian geometries | |
| dc.type | text |