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- Title
Curvature properties of some class of warped product manifolds.
- Authors
Deszcz, Ryszard; Głogowska, Małgorzata; Jełowicki, Jan; Zafindratafa, Georges
- Abstract
We prove that warped product manifolds with -dimensional base, satisfy some pseudosymmetry type curvature conditions. These conditions are formed from the metric tensor , the Riemann-Christoffel curvature tensor , the Ricci tensor and the Weyl conformal curvature of the considered manifolds. The main result of the paper states that if and the fiber is a semi-Riemannian space of constant curvature (when is greater or equal to 5) then the -tensors and of such warped products are proportional to the -tensor and the tensor is a linear combination of some Kulkarni-Nomizu products formed from the tensors and . We also obtain curvature properties of this kind of quasi-Einstein and 2-quasi-Einstein manifolds, and in particular, of the Goedel metric, generalized spherically symmetric metrics and generalized Vaidya metrics.
- Subjects
CURVATURE; MANIFOLDS (Mathematics); WEYL space; RIEMANNIAN manifolds; SPACES of constant curvature; EINSTEIN manifolds
- Publication
International Journal of Geometric Methods in Modern Physics, 2016, Vol 13, Issue 1, p-1
- ISSN
0219-8878
- Publication type
Article
- DOI
10.1142/S0219887815501352