Turkish Journal of Analysis and Number Theory

4

Authors: T. Satyanarayana, K. L. Sai Prasad

In this paper we study some remarkable properties 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 shown that a semi-symmetric p-Kenmotsu manifold (Mn, g) is of constant curvature and hence is 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 the Weyl projective semi-symmetric p-Kenmotsu manifold is projectively flat. Finally we prove that if the condition P(X,Y).R=0 is satisfied on a p-Kenmotsu manifold then its scalar curvature is constant.