Investigation of soliton structures on a tangent bundle with a semi-symmetric metric connection

Let us consider [Formula: see text] as the tangent bundle of a (pseudo-)Riemannian manifold [Formula: see text] equipped with a semi-symmetric metric connection [Formula: see text]. The goal of this research paper is to establish the necessary and sufficient conditions for the tangent bundle [Formula: see text] to become a Ricci soliton, gradient Ricci soliton, Riemannian soliton and generalized Ricci–Yamabe soliton with regard to [Formula: see text].