- International Electronic Journal of Geometry
- Vol: 16 Issue: 1
- On the Geometry of Tangent Bundle and Unit Tangent Bundle with Deformed-Sasaki Metric
On the Geometry of Tangent Bundle and Unit Tangent Bundle with Deformed-Sasaki Metric
Authors : Abderrahım Zagane
Pages : 132-146
Doi:10.36890/iejg.1182395
View : 6 | Download : 2
Publication Date : 2023-04-30
Article Type : Research
Abstract :Let $(M^{m}, g)$ be a Riemannian manifold and $TM$ its tangent bundle equipped with a deformed Sasaki metric. In this paper, firstly we investigate all forms of Riemannian curvature tensors of $TM$ (Riemannian curvature tensor, Ricci curvature, sectional curvature and scalar curvature). Secondly, we study the geometry of unit tangent bundle equipped with a deformed Sasaki metric, where we presented the formulas of the Levi-Civita connection and also all formulas of the Riemannian curvature tensors of this metric.Keywords : Tangent bundle, deformed-Sasaki metric, unit tangent bundle, curvature tensor