Communications of the
Korean Mathematical Society CKMS

In this paper, we introduce the Berger type deformed Sasaki metric on the cotangent bundle $T^{\ast}M$ over an anti-paraK\"{a}hler manifold $(M, \varphi, g)$ as a new natural metric with respect to $g$ non-rigid on $T^{\ast}M$. Firstly, we investigate the Levi-Civita connection of this metric. Secondly, we study the curvature tensor and also we characterize the scalar curvature.

Keywords: Horizontal lift, vertical lift, cotangent bundles, Berger type deformed Sasaki metric, curvature tensor

MSC numbers: 53C07, 53C55, 53B35, 53A45

Supported by: This note was supported by National Algerian PRFU project.