$2-$conformal and conformal vector fields on Riemannian manifolds

Abstract

‎In this paper, we study ‎$‎2-‎$‎‏conformal vector fields on Riemannian manifolds. Some relations between ‎$‎2-‎$‎‏conformal vector fields‎, ‎conformal vector fields, Killing and ‎$‎2-‎$‎‏Killing vector fields ‎has been obtained‎. ‎Also, ‎relation ‎between ‎monotone ‎vector ‎fields ‎and‎ ‎$‎2-$conformal vector fields is investigated. We give the characterization of ‎$‎2-$conformal vector fields on standard Euclidean spaces. Finally, examples of ‎such ‎vector ‎fields ‎on ‎some Riemannian ‎manifolds ‎is ‎presented.‎