Properties of modified Riemannian extensions

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Let M be an n-dimensional differentiable manifold with a symmetric connection ∇ and T be its cotangent bundle. In this paper, we study some properties of the modified Riemannian extension % g∇,c on T defined by means of a symmetric % (0,2)-tensor field c on M. We get the conditions under which T endowed with the horizontal lift ʰJ of an almost complex structure J and with the metric g∇,c is a Kähler-Norden manifold. Also curvature properties of the Levi-Civita connection and another metric connection of the metric g∇,c are presented.