Characterizing ϕRic-Vector Fields and Quasi-Einstein Manifolds on Multiply Warped Product Manifolds

Abstract

We characterize multiply warped product manifolds with ϕRic-vector fields. We give the necessary and sufficient conditions for the lift of a vector field on a factor manifold to be the ϕRic-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.