The Schouten-Van Kampen connection on the cotangent bundle with Sasaki metric

Source abstract

The purpose of this paper is to investigate the Schouten-Van Kampen connection associated with the Levi-Civita connection of the Sasaki metric on the cotangent bundle. We explicitly construct this connection and compute its curvature tensor and scalar curvature. Furthermore, we study the geodesics with respect to this connection and show that the given almost product structure is parallel. Finally, we prove that the Vranceanu connection associated with the Levi-Civita connection of the Sasaki metric coincides with the horizontal lift of any connection on the cotangent bundle.