On Semi-symmetric Para Kenmotsu Manifolds

T. Satyanarayana¹ and K. L. Sai Prasad^2,

¹Department of Mathematics, Pragathi Engineering College, Surampalem, Andhra Pradesh, India

²Department of Mathematics, Gayatri Vidya Parishad College of Engineering for Women, Visakhapatnam, Andhra Pradesh, India

Cite this paper:
T. Satyanarayana and K. L. Sai Prasad. On Semi-symmetric Para Kenmotsu Manifolds. Turkish Journal of Analysis and Number Theory. 2015; 3(6):145-148. doi: 10.12691/tjant-3-6-1

Abstract

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 (M_n, 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.

Keywords:
para Kenmotsu manifolds curvature tensor projective curvature tensor scalar curvature

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