We investigate several interesting characteristics of para Kenmotsu (briefly p-Kenmotsu) manifolds satisfying the conditions R(X,Y) . R = 0, R(X,Y) . P = 0 and P(X,Y) . R = 0, where R(X,Y) is the Riemannian curvature tensor and P(X,Y) is the Weyl projective curvature tensor of the manifold. It is demonstrated that a semi symmetric p-Kenmotsu manifold (Mn,g) has constant curvature and hence an sp-Kenmotsu manifold. Also we obtain the necessary and sufficient condition for a p-Kenmotsu manifold to be Weyl projective semi-symmetric and shown that it is projectively flat. Finally, we prove if the condition P(X,Y) . R = 0 is satisfied on a p-Kenmotsu manifold then its scalar curvature is constant.