Kyungpook Mathematical Journal 2015; 55(1): 149-156
Published online March 23, 2015
Copyright © Kyungpook Mathematical Journal.
Some Symmetric Properties on $(LCS)_{n}$-manifolds
Venkatesha and Rahuthanahalli Thimmegowda Naveen Kumar
Department of Mathematics, Kuvempu University, Shankaraghatta -577 451,\ Shimoga, Karnataka, India
We analyze the $(LCS)_{n}$-manifolds endowed with some symmetric properties, focusing on Ricci tensor and the $1$-form $gamma$. We study some properties of special Weakly Ricci-Symmetric $(LCS)_{n}$-manifolds and also shown that Weakly
$phi$-Ricci Symmetric $(LCS)_{n}$-manifold is an $eta$-Einstein manifold.
Keywords: Lorentzian metric, ,Ricci tensor, Einstein manifold, Weakly Ricci-symmetric, ,Weakly $phi$-Ricci Symmetric