In this paper, we investigate geodesics of the tangent bundle $TM$ of a Riemannian manifold $(M,g)$ endowed with an arbitrary pseudo-Riemannian $g$-natural metric of Kaluza-Klein type. Then considering a class of naturally defined almost complex structures on $TM$, constructed by V. Oproiu, we construct a class of magnetic fields and we characterize the corresponding magnetic curves on $TM$, when $(M,g)$ is a space form.
Tangent bundle, $g$-natural metric, metric of Kaluza-Klein type, geodesic, magnetic curve
ABBASSI, MOHAMED TAHAR KADAOUI and AMRI, NOURA
"Geodesics and natural complex magnetic trajectories on tangent bundles,"
Turkish Journal of Mathematics: Vol. 47:
2, Article 15.
Available at: https://journals.tubitak.gov.tr/math/vol47/iss2/15