Characterizing <i>ϕ</i> (Ric)‐Vector Fields and Quasi‐Einstein Manifolds on Multiply Warped Product Manifolds

We characterize multiply warped product manifolds with ϕ (Ric)‐vector fields. We give the necessary and sufficient conditions for the lift of a vector field on a factor manifold to be the ϕ (Ric)‐vector field. In terms of physical applications, the multiply generalized Robertson–Walker spacetime is considered. Moreover, we investigate the effect of the quasi‐Einstein condition on the factor manifolds of a multiply product. Additionally, it obtains conditions for a multiply warped product manifold satisfying the quasi‐Einstein condition to be a direct product manifold.