Authors: Abderrahim Zagane

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.

• 53C05 - Connections (general theory)
• 53C15 - General geometric structures on manifolds (almost complex, almost product structures, etc.)
• 53C22 - Geodesics in global differential geometry
• 53C55 - Global differential geometry of Hermitian and Kählerian manifolds