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The object of the present paper is to rectify the example in Section 5 and nullify the Theorem 5.1. 1. Remark In [1], the authors have stated that: (a) [1, Theorem 5.1, p. 306] “Let us consider a Lorentzian metric g on R by ds = gijdx dx = x [( dx )2 + ( dx )2 + ( dx )2]− (dx4)2 , where i, j = 1, 2, 3, 4. Then (R, g) is a weakly symmetric spacetime whose scalar curvature is non-zero and non-constant”. But statement (a) is found to be false. Let us recall the definition of a weakly symmetric manifold. A non-flat Riemannian manifold is called a weakly symmetric manifold if it realizes the relation (1.2) of [1, p. 300]. The local expression of the relation (1.2) of [1, p. 300], is (1.1) Rhijk,l = AlRhijk + DhRlijk + DiRhljk + DjRhilk + DkRhijl, where Al and Dl are two non-zero co-vectors and comma followed by indices denotes the covariant differentiation with respect to the metric tensor g. An n-dimensional manifold of this kind is denoted by WSn.

A remark on the paper 'On Weakly Symmetric Spacetimes' (Kragujevac J. Math. 36(2) (2012), 299-308)