We give necessary and sufficient conditions for warped product manifolds (M, g), of
dimension\geqslant 4, with 1-dimensional base, and in particular, for generalized Robertson-
-Walker spacetimes, to satisfy some generalized Einstein metric condition. Namely, the
difference tensor R. CC. R, formed from the curvature tensor R and the Weyl conformal
curvature tensor C, is expressed by the Tachibana tensor Q (S, R) formed from the Ricci
tensor S and R. We also construct suitable examples of such manifolds. They are quasi …

We give necessary and sufficient conditions for warped product manifolds (M, g), of
dimension>= 4, with 1-dimensional base, and in particular, for generalized Robertson-
Walker spacetimes, to satisfy some generalized Einstein metric condition. Namely, the
difference tensor RC-CR, formed from the curvature tensor R and the Weyl conformal
curvature tensor C, is expressed by the Tachibana tensor Q (S, R) formed from the Ricci
tensor S and R. We also construct suitable examples of such manifolds. They are quasi …