Characterization of W_6-curvature tensor on Lorentzian para-Kenmotsu manifolds

Abstract

The aim of this study is to explore the characteristics of $n$-dimensional Lorentzian para-Kenmotsu \{briefly, ($LPK)_{n}$\} manifolds with $\mathcal{W}_{6}$-curvature tensor. Firstly, we explore ($LPK)_{n}$ manifold with the condition \(`\mathcal{W}_{6}(\mathtt{A}, \mathtt{B}, \mathtt{C}, \zeta) =0 \) and find that it is an Einstein manifold. Next, we consider the conditions of $\varPhi$-$\mathcal{W}_{6}$-symmetric, $\mathcal{W}_{6}$-semisymmetric, and $\varPhi$-$\mathcal{W}_{6}$-flat on the ($LPK)_{n}$ manifold. Moreover, an example has been constrcuted to verify the results. Lastly, we explain the condition \(\mathcal{W}_{6}(\mathtt{E}, \mathtt{F}).\mathcal{R} =0 \) on ($LPK)_{n}$ manifold that establishes $\omega$-Einstein manifold.