Classification of torqued vector fields and its applications to Ricci solitons

Abstract

Recently, the author defined torqued vector fields in [Kragujevac J. Math. 41(1) (2017), 93–103]. In this paper, we classify all torqued vector fields on Riemannian manifolds. Moreover, we investigate Ricci solitons with torqued potential fields. In particular, we prove that every Ricci soliton with torqued potential field is an almost quasi-Einstein manifold; and it is an Einstein manifold if and only if the potential field is a concircular vector field. Some related results on Ricci solitons are also obtained.