Title of article :
On generalized Robertson-Walker spacetimes satisfying some curvature condition
Author/Authors :
ARSLAN, KADRİ Uludag University - Art and Science Faculty - Department of Mathematics, Turkey , DESZCZ, RYSZARD Wroc law University of Environmental and Life Sciences - Department of Mathematics, Poland , EZENTAŞ, RIDVAN Uludag University - Art and Science Faculty - Department of Mathematics, Turkey , HOTLOS, MARIAN Wroc law University of Technology - Institute of Mathematics and Computer Science, Poland , MURATHAN, CENGİZHAN Uludag University - Art and Science Faculty - Department of Mathematics, Turkey
Abstract :
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 Einsteinmetric 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 − α g) ≤ 1, for some α ∈ R, or non-quasi-Einstein.
Keywords :
Warped product , generalized Robertson–Walker spacetime , Einstein manifold , quasi , Einstein manifold , essentially conformally symmetric manifold , Tachibana tensor , generalized Einstein metric condition , pseudosymmetry type curvature condition , Ricci , pseudosymmetric hypersurface
Journal title :
Turkish Journal of Mathematics
Journal title :
Turkish Journal of Mathematics
