Jacobi--Tsankov manifolds which are not 2-step nilpotent
| dc.creator | Brozos-Vazquez, M. | |
| dc.creator | Gilkey, P. | |
| dc.date | 2006-09-20 | |
| dc.date.accessioned | 2026-07-07T07:25:00Z | |
| dc.date.available | 2026-07-07T07:25:00Z | |
| dc.description | An algebraic curvature tensor A is said to be Jacobi-Tsankov if J(x)J(y)=J(y)J(x) for all x,y. This implies J(x)J(x)=0 for all x; necessarily A=0 in the Riemannian setting. Furthermore, this implies J(x)J(y)=0 for all x,y if the dimension is at most 13. We exhibit a 14-dimensional algebraic curvature tensor in signature (8,6) which is Jacobi--Tsankov but which has J(x)J(y) non 0 for some x,y. We determine the group of symmetries of this tensor and show that it is geometrically realizable by a wide variety of pseudo-Riemannian manifolds which are geodesically complete and have vanishing scalar Weyl invariants. Some of the manifolds in the family are symmetric spaces. Some are 0-curvature homogeneous but not locally homogeneous. | |
| dc.identifier | https://arxiv.org/abs/math/0609565 | |
| dc.identifier | http://arxiv.org/abs/math/0609565 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116585 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C20 | |
| dc.title | Jacobi--Tsankov manifolds which are not 2-step nilpotent | |
| dc.type | text |