ON WEAKLY m−PROJECTIVELY SYMMETRIC MANIFOLDS

for arbitrary vector fieldsX, Y , Z, U , V ∈ χ(Mn), whereD denotes the operator of covariant differentiation with respect to the Riemannian metric g and A, B, C, D and E are 1−forms (not simultaneously zero). The 1−forms are called the associated 1−forms of the manifold and an n−dimensional manifold of this kind is denoted by (WS)n. Tamassy and Binh [14] further studied weakly symmetric Sasakian manifolds and proved that such manifold does not always exits. In [3] the authors established the existence of (WS)n by an example and proved that in (WS)n, the associated 1−forms B = C and D = E. So (1.1) reduces to the following form