On the cotangent bundle of a differentiable manifold

We study some geometric properties of the cotangent bundle T*M of a differentiable manifold M, endowed with an arbitrary asymmetric nonlinear connection. It is obtained a pseudo-Riemannian metric G on T*M, of Riemann extension type, for which we study the conditions under which it is either flat, or projectively flat, or conformally flat or locally symmetric. Further, by using an almost complex structure J or an almost product structure P on T*M, defined by the same nonlinear connection and an M-tensor field on T*M, we obtain some results concerning the property of (T*M, J, G) (of (T*M, P, G)) to be a Kaehler manifold with Norden metric (to be a para-Kaehler manifold).