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Full-Text Articles in Physical Sciences and Mathematics
Geodesics And Isocline Distributions In Tangent Bundles Of Nonflat Lorentzian-Heisenberg Spaces, Murat Altunbaş
Geodesics And Isocline Distributions In Tangent Bundles Of Nonflat Lorentzian-Heisenberg Spaces, Murat Altunbaş
Turkish Journal of Mathematics
Let $(H_{3},g_{1})$ and $(H_{3},g_{2})$ be the Lorentzian-Heisenberg spaces with nonflat metrics $g_{1}$ and $g_{2},\ $and $(TH_{3},g_{1}^{s}),\ (TH_{3},g_{2}^{s})$ be their tangent bundles with the Sasaki metric, respectively. In the present paper, we find nontotally geodesic distributions in tangent bundles by using lifts of contact forms from the base manifold $H_{3}.$We give examples for totally geodesic but not isocline distributions. We study the geodesics of tangent bundles by considering horizontal and natural lifts of geodesics of the base manifold $H_{3}$. We also investigate more general classes of geodesics which are not obtained from horizontal and natural lifts of geodesics.
Geodesics And Natural Complex Magnetic Trajectories On Tangent Bundles, Mohamed Tahar Kadaoui Abbassi, Noura Amri
Geodesics And Natural Complex Magnetic Trajectories On Tangent Bundles, Mohamed Tahar Kadaoui Abbassi, Noura Amri
Turkish Journal of Mathematics
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.