Abderrahim Zagane, Nour Elhouda Djaa, Aydin Gezer

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In this paper, we consider a generalized Cheeger-Gromoll metric on a cotangent bundle over a Riemannian manifold, which is obtained by rescaling the vertical part of the Cheeger-Gromoll metric by a positive dierentiable function. Firstly, we investigate the curvature properties on the cotangent bundle with the generalized Cheeger-Gromoll metric. Secondly, we introduce the unit cotangent bundle equipped with this metric, where we present the formulas of the Levi-Civita connection and also all formulas of the Riemannian curvature tensors of this metric. Finally, we study the geodesics on the unit cotangent bundle with respect to this metric.


Horizontal lift and vertical lift, cotangent bundles, generalized Cheeger-Gromoll metric, curvature tensor.

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DOI: https://doi.org/10.22190/FUMI221101011Z


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