Let $M$ be an $n-$dimensional differentiable manifold with a symmetric connection $\nabla $ and $T^{ \ast}M$ be its cotangent bundle. In this paper, we study some properties of the modified Riemannian extension $% \widetilde{ g}_{ \nabla,c}$ on $T^{ \ast}M$ defined by means of a symmetric $% (0,2)$-tensor field $c$ on $M.$ We get the conditions under which $T^{ \ast}M $ endowed with the horizontal lift $^{ H}J$ of an almost complex structure $J$ and with the metric $\widetilde{ g}_{ \nabla,c}$ is a K\"{ a}hler-Norden manifold. Also curvature properties of the Levi-Civita connection and another metric connection of the metric $\widetilde{ g}_{ \nabla,c}$ are presented.
Categories: math.DG