Note on geodesics of cotangent bundle with Berger-type deformed Sasaki metric over Kählerian manifold

Abstract

In this paper, first, we introduce the Berger-type deformed Sasaki metric on the cotangent bundle $T^{\ast }M$ over a Kählerian manifold $(M^{2m},J,g)$ and investigate the Levi-Civita connection of this metric. Secondly, we present the unit cotangent bundle equipped with Berger-type deformed Sasaki metric, and we investigate the Levi-Civita connection. Finally, we study the geodesics on the cotangent bundle and on unit cotangent bundle with respect to the Berger-type deformed Sasaki metric.