Curvature properties of some class of warped product manifolds
Ryszard Deszcz , Małgorzata Głogowska , Jan Jełowicki , Georges Zafindratafa
AbstractWe 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.
|Journal series||International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, e-ISSN 1793-6977, [1793-6977], (A 25 pkt)|
|Publication size in sheets||0.3|
|Score|| = 20.0, 01-07-2020, ArticleFromJournal|
= 25.0, 01-07-2020, ArticleFromJournal
|Publication indicators||= 18; = 15; : 2016 = 0.7; : 2016 = 1.068 (2) - 2016=0.704 (5)|
|Citation count*||33 (2021-06-14)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.