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

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.

References

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