Czechoslovak Mathematical Journal, Vol. 71, No. 1, pp. 75-109, 2021
On $g$-natural conformal vector fields on unit tangent bundles
Mohamed Tahar Kadaoui Abbassi, Noura Amri
Received April 24, 2019. Published online August 17, 2020.
Abstract: We study conformal and Killing vector fields on the unit tangent bundle, over a Riemannian manifold, equipped with an arbitrary pseudo-Riemannian $g$-natural metric. We characterize the conformal and Killing conditions for classical lifts of vector fields and we give a full classification of conformal fiber-preserving vector fields on the unit tangent bundle endowed with an arbitrary pseudo-Riemannian Kaluza-Klein type metric.
Keywords: conformal vector field; unit tangent bundle; $g$-natural metric
Affiliations: Mohamed Tahar Kadaoui Abbassi (corresponding author), Noura Amri, Laboratory of Mathematical Sciences and Applications, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University Sidi Mohamed Ben Abdallah, B.P. 1796, Fès-Atlas, Fez, Morocco, e-mail: mtk_abbassi@Yahoo.fr, firstname.lastname@example.org