This article 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 ∇R = 0 is satisfied and it also admits the pseudosymmetric type curvature conditions C · R = (1+L0) 6r 2 0 Q(g, R) and P · R = − 1 3 Q(S, R). Moreover, it is 4-dimensional Roter type, 2-quasi-Einstein and generalized quasi-Einstein manifold. 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 a class of generalized recurrent type manifolds which is semisymmetric.2010 Mathematics Subject Classification. 53B20, 53B25, 53B30, 53B50, 53C15, 53C25, 53C35.