Turkish Journal of Mathematics
Abstract
We define in this note a natural metric over the tangent bundle $TM$ by using a vertical deformation of Sasaki metric. First we present the geometric result concerning the Levi-Civita connection and all forms of Riemannian curvature tensors of this metric. Secondly, we study the geodesics on the tangent bundle $TM$ and unit tangent bundle $T_{1}M$. Finally, we characterize the geodesic curvatures on $T_{1}M$.
DOI
10.55730/1300-0098.3258
Keywords
Deformed Sasaki metric, geodesics, tangent bundle, unit tangent bundle
First Page
2121
Last Page
2140
Recommended Citation
DJAA, N. E, & ZAGANE, A (2022). On the geodesics of deformed Sasaki metric. Turkish Journal of Mathematics 46 (6): 2121-2140. https://doi.org/10.55730/1300-0098.3258
