A study on the tangent bundle with the vertical generalized Berger type deformed Sasaki metric

Authors : Saadia Chaoui, Abderrahım Zagane, Aydın Gezer, Nour Elhouda Djaa

Pages : 1179-1197

Doi:10.15672/hujms.1091758

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Publication Date : 2023-10-31

Article Type : Research Paper

Abstract :In this paper, we introduce a vertical generalized Berger type deformed Sasaki metric on the tangent bundle $TM$ over an anti-paraK\\\"{a}hler manifold as a new natural metric. Firstly, we investigate the Levi-Civita connection of this metric and then we calculate all forms of the Riemannian curvature tensors. Also, we present some results concerning curvature properties. Finally, we study the geometry of $\\varphi $-unit tangent bundle equipped with the vertical generalized Berger type deformed Sasaki metric.
Keywords : Tangent bundle, anti paraK¨ahler manifolds, Riemannian curvature tensor, φ unit tangent bundle, vertical generalized Berger type deformed Sasaki metric