On generalized Robertson-Walker spacetimes satisfying some curvature condition

Arslan K., Deszcz R., Ezentaş R., Hotlos M., Murathan C.

TURKISH JOURNAL OF MATHEMATICS, cilt.38, sa.2, ss.353-373, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 2
  • Basım Tarihi: 2014
  • Doi Numarası: 10.3906/mat-1304-3
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.353-373
  • Anahtar Kelimeler: 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
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.