Some Notes on Berger Type Deformed Sasaki Metric in the Cotangent Bundle

Abstract

In the present paper, we study some notes on Berger type deformed Sasaki metric in the cotangent bundle T * M over an anti-paraKähler manifold (M, ϕ, g). We characterize some geodesic properties for this metric. Next we also construct some almost anti-paraHermitian structures on T * M and search conditions for these structures to be anti-paraKähler and quasi-anti-paraKähler with respect to the Berger type deformed Sasaki metric.

Geodesics on tangent bundles with horizontal Sasaki gradient metric

“…Definition 3.1. [28] Let (M 2m , ϕ, g) be a para-Kähler-Norden manifold. On the tangent bundle T M , we define a ϕ-Sasaki metric noted g ϕ by…”

“…Theorem 3.2. [28] Let (M 2m , ϕ, g) be a para-Kähler-Norden manifold and T M its tangent bundle equipped with the ϕ-Sasaki metric g ϕ . If ∇ (resp ∇) denote the Levi-Civita connection of (M 2m , ϕ, g) (resp (T M, g ϕ ) ), then we have…”

“…In previous works, [28,30], we proposed the ϕ-Sasaki metric on the tangent bundle over para-Kähler-Norden manifold (M 2m , ϕ, g), where we studied respectively the para-Kähler-Norden properties on the tangent bundle and then Geometry of ϕ-Sasaki metric on tangent bundle. In this paper, we investigate some geodesics and F -geodesics properties for the ϕ-Sasaki metric on the tangent bundle and on ϕ-unit tangent bundle.…”

On the Geometry of Tangent Bundle and Unit Tangent Bundle with Deformed-Sasaki Metric

“…The deformations of the Sasaki metric on the tangent bundle are not limited to those mentioned above. Also, we refer to [1,3,10,15,16,17].…”

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

“…The study of the Berger-type deformed Sasaki metric on the tangent bundle or on the cotangent are not limited to those mentioned above. We also refer to new studies by Zagane, A. among which we [15][16][17][18][19][20]. .…”