Geodesics and natural complex magnetic trajectories on tangent bundles

Authors: MOHAMED TAHAR KADAOUI ABBASSI, NOURA AMRI

Abstract: 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.

Keywords: Tangent bundle, $g$-natural metric, metric of Kaluza-Klein type, geodesic, magnetic curve

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