Geometry of $\varphi$-Unit Tangent Bundle with Vertical Rescaled Berger Deformation Metric

Abstract

In this paper, we talk about the vertical rescaled Berger deformation metric on the $\varphi$-unit tangent bundle over an anti-paraK\"{a}hler manifold $(M^{2m}, \varphi, g)$. Firstly, we investigate the Levi-Civita connection in this metric. Secondly, we calculate all forms of the Riemannian curvature tensors. Finally, we study the geodesics on the $\varphi$-unit tangent bundle concerning the vertical rescaled Berger deformation metric.

Keywords

• $\varphi$-unit tangent bundle
• vertical rescaled Berger deformation metric
• anti-paraK\"{a}hler manifold
• geodesics

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