eng
Science and Education Publishing
Turkish Journal of Analysis and Number Theory
2333-1232
2015-12-18
3
6
145
148
10.12691/tjant-3-6-1
TJANT2015361
article
On Semi-symmetric Para Kenmotsu Manifolds
T. Satyanarayana
1
K. L. Sai Prasad
klsprasad@yahoo.com
2
Department of Mathematics, Pragathi Engineering College, Surampalem, Andhra Pradesh, India
Department of Mathematics, Gayatri Vidya Parishad College of Engineering for Women, Visakhapatnam, Andhra Pradesh, India
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.
http://pubs.sciepub.com/tjant/3/6/1/tjant-3-6-1.pdf
para Kenmotsu manifolds
curvature tensor
projective curvature tensor
scalar curvature