A Note on Generalized Quasi-Einstein and (λ, n + m)-Einstein Manifolds with Harmonic Conformal Tensor

Sufficient conditions for a Lorentzian generalized quasi-Einstein manifold M,g,f,μ to be Robertson–Walker spacetime with Einstein fibers are derived. The Ricci tensor in this case gains the perfect fluid form. Likewise, it is proven that λ,n+m-Einstein M,g,w having harmonic Weyl tensor, ∇jw∇mwCjklm=0 and ∇lw∇lw<0 reduces fibers. Finally, if φ=−m∇lnw φRic-vector field on M an ψ=∇w ψRic-vector M. Some consequences of these results considered.