On a class of paracontact Riemannian manifold

Document Type : Research Paper


Department of Mathematics, Faculty of Science, Arak university, Arak 38156-8-8349, Iran


We classify the paracontact Riemannian manifolds that their Riemannian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.