- Turkish Journal of Mathematics
- Vol: 38 Issue: 2
- On generalized Robertson--Walker spacetimes satisfying some curvature condition
On generalized Robertson--Walker spacetimes satisfying some curvature condition
Authors : Kadri Arslan, Ryszard Deszcz, Ridvan Ezentas, Marian Hotlos, Cengizhan Murathan
Pages : 353-373
Doi:10.3906/mat-1304-3
View : 11 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :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 . 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 - a g) \leqslant 1, for some a \in 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-pseud