Harmonic sections of tangent bundles equipped with Riemannian $g$-natural metrics
| dc.creator | Abbassi, M. T. K. | |
| dc.creator | Calvaruso, G. | |
| dc.creator | Perrone, D. | |
| dc.date | 2007-10-19 | |
| dc.date.accessioned | 2026-07-07T08:37:19Z | |
| dc.date.available | 2026-07-07T08:37:19Z | |
| dc.description | Let $(M,g)$ be a Riemannian manifold. When $M$ is compact and the tangent bundle $TM$ is equipped with the Sasaki metric $g^s$, the only vector fields which define harmonic maps from $(M,g)$ to $(TM,g^s)$, are the parallel ones. The Sasaki metric, and other well known Riemannian metrics on $TM$, are particular examples of $g$-natural metrics. We equip $TM$ with an arbitrary Riemannian $g$-natural metric $G$, and investigate the harmonicity of a vector field $V$ of $M$, thought as a map from $(M,g)$ to $(TM,G)$. We then apply this study to the Reeb vector field and, in particular, to Hopf vector fields on odd-dimensional spheres. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/0710.3668 | |
| dc.identifier | http://arxiv.org/abs/0710.3668 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140362 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C43, 53C07,53C15,53D10 | |
| dc.title | Harmonic sections of tangent bundles equipped with Riemannian $g$-natural metrics | |
| dc.type | text |