Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2015, 3(6), 145-148
DOI: 10.12691/tjant-3-6-1
Open AccessArticle

On Semi-symmetric Para Kenmotsu Manifolds

T. Satyanarayana1 and K. L. Sai Prasad2,

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

Pub. Date: December 18, 2015

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 (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.

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

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