some results of ricci bi-conformal vector fields

‎the investigation of ricci bi-conformal vector fields and their associated outcomes is crucial for gaining insights into the geometric and topological characteristics of the underlying manifolds‎. ‎the study of conformal vector fields and their extensions is highly valuable in the realms of geometry and physics‎. ‎in this manuscript‎, ‎we study the topological properties of the ricci bi-conformal vector field‎. ‎the goal of this paper is to find some results of the ricci bi-conformal vector fields‎. ‎we prove that a complete manifold admits the ricci bi-conformal vector fields has a finite fundamental group‎. ‎for this purpose‎, ‎we first state the definition and lemma‎, ‎and then use them to prove our theorems‎.