DOI: 10.3390/axioms12090809 ISSN:
A Solitonic Study of Riemannian Manifolds Equipped with a Semi-Symmetric Metric ξ-Connection
Abdul Haseeb, Sudhakar Kumar Chaubey, Fatemah Mofarreh, Abdullah Ali H. Ahmadini- Geometry and Topology
- Logic
- Mathematical Physics
- Algebra and Number Theory
- Analysis
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.