On the rescaled Riemannian metric of Cheeger-Gromoll type on the cotangent bundle

Abstract

Let (M, g) be an n−dimensional Riemannian manifold and T ∗M be its cotangent bundle equipped with a Riemannian metric of CheegerGromoll type which rescale the horizontal part by a positive differentiable function. The main purpose of the present paper is to discuss curvature properties of T ∗M and construct almost paracomplex Norden structures on T ∗M. We investigate conditions for these structures to be para-Kähler (paraholomorphic) and quasi-para-Kähler. Also, some properties of almost paracomplex Norden structures in context of almost product Riemannian manifolds are presented.