Curvature properties of some class of warped product manifolds - Université Polytechnique des Hauts-de-France Access content directly
Journal Articles International Journal of Geometric Methods in Modern Physics Year : 2016

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.
Fichier principal
Vignette du fichier
1507.02915.pdf (427.74 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03148376 , version 1 (05-07-2022)

Identifiers

Cite

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, 2016, 13 (01), pp.1550135. ⟨10.1142/S0219887815501352⟩. ⟨hal-03148376⟩
34 View
13 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More