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

الأصل · EN

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