A Solitonic Study of Riemannian Manifolds Equipped with a Semi-Symmetric Metric ξ -Connection.

The aim of this paper is to characterize a Riemannian 3-manifold M 3 equipped with a semi-symmetric metric ξ -connection ∇ ˜ with ρ -Einstein and gradient ρ -Einstein solitons. The existence of a gradient ρ -Einstein soliton in an M 3 admitting ∇ ˜ is ensured by constructing a non-trivial example, and hence some of our results are verified. By using standard tensorial technique, we prove that the scalar curvature of (M 3 , ∇ ˜) satisfies the Poisson equation Δ R = 4 (2 − σ − 6 ρ) ρ . [ABSTRACT FROM AUTHOR]