On weakly symmetric Riemannian manifolds F.Malek and M.Samavaki Abstract. In this paper its proved three theorems about weakly symmet- ric manifolds. The first one is a sufficiency condition for a (WS) n to be a G(PS) n and a (PS) n . The second one is about the Ricci tensor of a conformally flat (WS) n with non zero scalar curvature, and the last one is about (WS) n with cyclic Ricci tensor. M.S.C. 2000: 53C21, 57N16, 35S99. Key words: curvature tensor, Ricci tensor, scalar curvature, comformally flat mani- fold. Introduction A pseudo symmetric manifold which was introduced in [3] is a non-flat Riemannian manifold V n (n> 2) in which the curvature tensor R hijk satisfies the condition R hijk,l =2A l R hijk + A h R lijk + A i R hljk + A j R hilk + A k R hijl , where A is a non-zero 1-form and , , , denotes covariant differentiation with respect to the metric tensor of the manifold and A is called it’s associated 1-form. The n-dimensional manifolds of this kind are denoted by (PS) n . A Generalized pseudo symmetric manifold was which introduced in [1] is a non- flat Riemannian manifold V n (n> 2) in which the curvature tensor R hijk satisfies the condition R hijk,l =2A l R hijk + B h R lijk + C i R hljk + D j R hilk + A k R hijl , where A, B, C and D are 1-forms (non-zero simultaneously). The n-dimensional manifolds of this kind are denoted by G(PS) n . Its shown in [2], the defining condition of a G(PS) n can be expressed in the following form R hijk,l =2A l R hijk + B h R lijk + B i R hljk + A j R hilk + A k R hijl , where A and B are 1-forms (non-zero simultaneously) and are called the associated 1-forms of the manifold. Differential Geometry - Dynamical Systems, Vol.10, 2008, pp. 215-220. c  Balkan Society of Geometers, Geometry Balkan Press 2008.