On metric connections with torsion on the cotangent bundle with modified Riemannian extension

Let M be an n-dimensional differentiable manifold equipped with a torsion-free linear connection del and T*M its cotangent bundle. The present paper aims to study a metric connection (del) over tilde. with nonvanishing torsion on T*M with modified Riemannian extension (g) over bar (del),(c). First, we give a characterization of fibre-preserving projective vector fields on (T*M, (g) over bar (del),(c)) with respect to the metric connection (del) over tilde. Secondly, we study conditions for (T*M, (g) over bar (del),(c)) to be semi-symmetric, Ricci semi-symmetric, (Z) over tilde semi-symmetric or locally conharmonically flat with respect to the metric connection (del) over tilde.. Finally, we present some results concerning the Schouten-Van Kampen connection associated to the Levi-Civita connection (del) over bar of the modified Riemannian extension (g) over bar (del),(c).