Ricci soliton, conformal Ricci soliton and torqued vector fields

Abstract

In this paper, we discussed the torqued vector field and did some applications of a torqued vector field on conformal Ricci soliton. We proved that if the potential field of a conformal Ricci soliton is a torqued vector field Ƭ, then (M, g) is an almost quasi-Einstein manifold. We also dealt with multiply warped products. We showed that a conformal Ricci soliton with torqued potential field Ƭ is Einstein if and only if Ƭ is a concircular vector field. We also studied Ricci's soliton on multiply warped product space admitting canonical torqued potential field.