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

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International Electronic Journal of Geometry
Volume: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

Pages : 132-146

View : 52 | Download : 10

Publication Date : 2023-04-30

Article Type : Research Paper

Abstract :Let $insert ignore into journalissuearticles values(M^{m}, g);$ 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 $TM$ insert ignore into journalissuearticles values(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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