Curvature and Solitonic Structures of Para-Sasakian Manifolds With Schouten–van Kampen Connection on the Tangent Bundle

This paper investigates the complete lift of para-Sasakian structures to the tangent bundle equipped with the Schouten–van Kampen connection (SVKC). By analyzing curvature tensors and soliton equations, we establish the existence of Ricci, Yamabe, and η-Ricci solitons in the lifted setting. It is proved that the lifted manifold retains key geometric properties under the SVKC. These results are illustrated through an explicit 5-dimensional example using partial differential equations that satisfy the soliton equations, offering new insights into geometric flows on lifted paracontact manifolds and laying a foundation for future extensions involving conformal solitons, higher-order bundles, and Lorentzian geometries.