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 have 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.