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
Turkish Journal of Analysis and Number Theory.
2015,
Vol. 3 No. 6, 145-148
DOI: 10.12691/tjant-3-6-1
Copyright © 2015 Science and Education PublishingCite this paper: T. Satyanarayana, 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.
Correspondence to: K. L. Sai Prasad, Department of Mathematics, Gayatri Vidya Parishad College of Engineering for Women, Visakhapatnam, Andhra Pradesh, India. Email:
klsprasad@yahoo.comAbstract
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.
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