Certain results of $(LCS)_{n}$-manifolds endowed with $E$-Bochner curvature tensor

Abstract

In this paper, we study geometry of $(LCS)_{n}$-manifold focusing on some conditions of $E$-Bochner curvature tensor. First, we describe an $E$-Bochner pseudo-symmetric $(LCS)_{n}$-manifold is never reduces to $E$-Bochner semi-symmetric manifold under the condition ($(\alpha^{2}-\rho)\neq0$). Next, we characterize certain results of $(LCS)_{n}$-manifold satisfying $B^{e}(U,V)\xi=0$, $B^{e}(\xi,V)\cdot B^{e}=0$ and $B^{e}(\xi,V)\cdot S=0$.