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

Let (M, g) be an n-dimensional Riemannian manifold and T* M be its cotangent bundle equipped with a Riemannian metric of Cheeger-Gromoll 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-Kahler (paraholomorphic) and quasi-para-Kahler. Also, some properties of almost paracomplex Norden structures in context of almost product Riemannian manifolds are presented.