On the Geometry of Tangent Bundle and Unit Tangent Bundle with Deformed-Sasaki Metric

Year 2023, , 132 - 146, 30.04.2023

Abderrahım Zagane

https://doi.org/10.36890/iejg.1182395

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

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