Characterization of three-dimensional Riemannian manifolds with a type of semi-symmetric metric connection admitting Yamabe soliton

Abstract

We characterize the three-dimensional Riemannian manifolds equipped with a semi-symmetric metric ρ-connection under the assumption that the Riemannian metric is a Yamabe soliton. It is shown that a three-dimensional Riemannian manifold endowed with a semi-symmetric ρ-connection, whose metric is Yamabe soliton, is a manifold of constant sectional curvature −1 and the Yamabe soliton is expanding with soliton constant −6. Finally, we give an example of a three-dimensional Riemannian manifold and validate our findings.