Relating the curvature tensor and the complex Jacobi operator of an almost Hermitian manifold
| dc.creator | Brozos-Vazquez, M. | |
| dc.creator | Garcia-Rio, E. | |
| dc.creator | Gilkey, P. | |
| dc.date | 2006-11-20 | |
| dc.date.accessioned | 2026-07-07T07:33:08Z | |
| dc.date.available | 2026-07-07T07:33:08Z | |
| dc.description | Let J be a unitary almost complex structure on a Riemannian manifold (M,g). If x is a unit tangent vector, let P be the associated complex line spanned by x and by Jx. We show that if (M,g) is Hermitian or if (M,g) is nearly Kaehler, then either the complex Jacobi operator (JC(P)y=R(y,x)x+R(y,Jx)Jx) or the complex curvature operator (RC(P)y=R(x,Jx)y) completely determine the full curvature operator; this generalizes a well known result in the real setting to the complex setting. We also show this result fails for general almost Hermitian manifold. | |
| dc.identifier | https://arxiv.org/abs/math/0611605 | |
| dc.identifier | http://arxiv.org/abs/math/0611605 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119353 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C15; 53C55 | |
| dc.title | Relating the curvature tensor and the complex Jacobi operator of an almost Hermitian manifold | |
| dc.type | text |