On generalized robertson-walker spacetimes satisfying some curvature condition
Loading...
Date
2014
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
TÜBİTAK
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 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.
Description
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, Hypersurfaces, Geometry, Mathematics
Citation
Arslan, K. vd. (2014). "On generalized robertson-walker spacetimes satisfying some curvature condition". Turkish Journal of Mathematics, 38(2), 353-373.