Special linear connections on the cotangent bundle with respect to the Cheeger-Gromoll metric

Let $(M,g)$ be an n-dimensional differentiable Riemannian manifold and $T^*M$ be its cotangent bundle equipped with the Cheeger-Gromoll metric ${}^{CG}g$. In this article, we investigate some applications of special linear connections, such as the Schouten-Van Kampen and Vr\u{a}nceanu connections associated with the Levi-Civita connection of the Cheeger-Gromoll metric ${}^{CG}g$ on $T^*M$.