Some Notes on Geodesics of Vertical Rescaled Berger Deformation Metric in Tangent Bundle

Abstract

In this paper, we study the geodesics on the tangent bundle $TM$ with respect to the vertical rescaled Berger deformation metric over an anti-paraK\"{a}hler manifold $(M, \varphi, g)$. In this case, we establish the necessary and sufficient conditions under which a curve be geodesic with respect to this. Finally, we also present certain examples of geodesic.