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Curvature properties of some class of warped product manifolds

Abstract : We prove that warped product manifolds with p-dimensional base, p=1,2, satisfy some pseudosymmetry type curvature conditions. These conditions are formed from the metric tensor g, the Riemann–Christoffel curvature tensor R, the Ricci tensor S and the Weyl conformal curvature C of the considered manifolds. The main result of the paper states that if p=2 and the fiber is a semi-Riemannian space of constant curvature (when n is greater or equal to 5) then the (0,6)-tensors R⋅R−Q(S,R) and C⋅C of such warped products are proportional to the (0,6)-tensor Q(g,C) and the tensor C is a linear combination of some Kulkarni–Nomizu products formed from the tensors g and S. 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.
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Submitted on : Monday, February 22, 2021 - 11:02:32 AM
Last modification on : Tuesday, October 19, 2021 - 6:38:17 PM

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Ryszard Deszcz, Małgorzata Głogowska, Jan Jełowicki, Georges Zafindratafa. Curvature properties of some class of warped product manifolds. International Journal of Geometric Methods in Modern Physics, World Scientific Publishing, 2016, 13 (01), pp.1550135. ⟨10.1142/S0219887815501352⟩. ⟨hal-03148376⟩

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