Chand De, U.Shenawy, S.Ünal, Bülent2022-02-162022-02-162021-11http://hdl.handle.net/11693/77423Sufficient and necessary conditions are provided on warped product manifolds and their base and fiber manifolds for a vector field φj to be a φ(Ric)-vector field , that is, ∇iφj=μRij where Rij is the Ricci tensor of M and μ is a scalar. Two warped product space-times admitting φ(Ric)-vector fields are considered. Lorentzian quasi-Einstein manifolds admitting a time-like φ(Ric)-vector field are shown to be either Ricci simple or a perfect fluid GRW space-time. The generators of a Lorentzian generalized quasi-Einstein manifold admitting a time-like φ(Ric)-vector field are eigenvectors of the Ricci tensor with zero eigenvalue.Englishϕ (Ric)-vector fieldQuasi-EinsteinPerfect fluidGeneralized Robertson–Walker space-timeArticle10.1007/s13370-021-00930-5