On natural symmetries on slit tangent bundles of Finsler manifolds

Mohamed Tahar Kadaoui Abbassi; Abderrahim Mekrami

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arXiv · 2411.06580

On natural symmetries on slit tangent bundles of Finsler manifolds

Mohamed Tahar Kadaoui Abbassi·Abderrahim Mekrami

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Abstract

In this paper, we introduce a broad class of metrics on the slit tangent bundle of Finsler manifolds, termed \emph{$F$-natural metrics}. These metrics parallel the well-established $g$-natural metrics on the tangent bundles of Riemannian manifolds and are constructed using six real functions defined over the domain of positive real numbers. We provide an in-depth characterization of conformal, homothetic, and Killing vector fields derived from specific lifts of vector fields and tensor sections on the slit tangent bundle, which is equipped with a general pseudo-Riemannian $F$-natural metric.

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Mohamed Tahar Kadaoui Abbassi, Abderrahim Mekrami. 2024-11-10. On natural symmetries on slit tangent bundles of Finsler manifolds. https://arxiv.org/abs/2411.06580

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