Abstract
This paper is concerned with the study of the geometry of (charged) Nariai spacetime, a topological product spacetime, by means of covariant derivative(s) of its various curvature tensors. It is found that on this spacetime the condition del R = 0 is satisfied and it also admits the pseudosymmetric type curvature conditions C . R = (1+L-0)/6r(0)(2)Q(g, R) and P . R = -1/3Q(S, R). Moreover, it is 4-dimensional Roter type, 2-quasi-Einstein and generalized quasi-Einstein spacetime. The energy momentum tensor is expressed explicitly by some 1-forms. It is worthy to see that a generalization of such topological product spacetime proposes to exist with a class of generalized recurrent type manifolds which is semisymmetric. It is observed that the rank of (S-alpha g), alpha = -1/r(0)(2), of Nariai spacetime (NS) is 0 whereas in case of charged Nariai spacetime (CNS) it is 2, which exhibits that effects of charge increase the rank of Ricci tensor. Also, due to the presence of charge in CNS, it gives rise to the proper pseudosymmetric type geometric structures.