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

Abstract

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

References in corpus (1)

• The Srni lectures on non-integrable geometries with torsion

Cited by in corpus (1)

• Note on geodesics of cotangent bundle with Berger-type deformed Sasaki metric over Kählerian manifold