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

Abstract

The aim of this paper is to characterize a Riemannian 3-manifold M3 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 M3 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 (M3,∇˜) satisfies the Poisson equation ΔR=4(2−σ−6ρ)ρ.