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

Year 2016, Volume: 45 Issue: 2, 355 - 365, 01.04.2016

Aydin Gezer , Murat Altunbas

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. 

Keywords

Almost paracomplex structure, connection, cotangent bundle, paraholomorphic tensor field, Riemannian metric

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