Deszcz, RyszardHotloś, Marian2022-08-252022-08-252014Arslan, K. vd. (2014). "On generalized robertson-walker spacetimes satisfying some curvature condition". Turkish Journal of Mathematics, 38(2), 353-373.1300-00981303-6149https://doi.org/10.3906/mat-1304-3https://dergipark.org.tr/tr/pub/tbtkmath/article/145666http://hdl.handle.net/11452/28353We 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 R.C-C.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-Einstein, i.e. at every point of M rank (S - alpha g) <= 1, for some alpha is an element of R, or non-quasi-Einstein.eninfo:eu-repo/semantics/openAccessWarped productGeneralized Robertson-Walker spacetimeEinstein manifoldQuasi-Einstein manifoldEssentially conformally symmetric manifoldTachibana tensorGeneralized Einstein metric conditionPseudosymmetry type curvature conditionRicci-pseudosymmetric hypersurfaceHypersurfacesGeometryMathematicsArticle0003336574000162-s2.0-84893341808353373382MathematicsWarped Product; Kaehler Manifold; Sasakian Space Form