Boletim da Sociedade Paranaense de Matematica, cilt.42, 2024 (ESCI)
Let M be an n-dimensional differentiable manifold with a torsion-free linear connection ∇ which induces on its cotangent bundle T*M. The main purpose of the present paper is to study some properties of the vertical modified Riemannian extension on T*M which is given as a new metric in [17]. At first, we investigate a metric connection with torsion on T*M. And then, we present the holomorphy properties with respect to a compatible almost complex structure. Furthermore, we study locally decomposable Golden pseudo-Riemannian structures on the cotangent bundle endowed with vertical modified Riemannian extension.