Some important characteristics of $W_8$- and $W_9$-curvature tensors on Lorentzian para-Kenmotsu manifolds along
semi-symmetric metric connection
Rajendra PRASAD, Sushmita SEN
Received December 11, 2024. Published online February 6, 2026.
Abstract: This paper deals with the study of $W_8$-curvature tensor and $W_9$-curvature tensor in Lorentzian para-Kenmotsu manifold (briefly, (LPK)$_n$) along semi-symmetric metric connection. First, we explore the $\overlineW_8$-flat-curvature tensor on (LPK)$_n$ manifold along semi-symmetric metric connection, which establishes $\eta$-Einstein manifold. Moreover, we have studied $\xi$-$\overlineW_8$-flat, $\overlineW_8$-semi-symmetric, $\overlineW_8{\cdot}\overlineQ = 0$, and $\overlineW_8{\cdot}\overlineR$. From all these, we have found $\eta$-Einstein manifold. Further, we have explored $\overlineW_9$-flat-curvature tensor, \hbox{$\xi$-$\overlineW_9$-flat}, $\overlineW_9$-semi-symmetric, and $\overlineW_9{\cdot}\overlineQ = 0$; from all these, we have established $\eta$-Einstein manifold.
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Affiliations: Rajendra Prasad, Sushmita Sen (corresponding author), Department of Mathematics and Astronomy, University of Lucknow, Lucknow, Uttar Pradesh 226007, India, email: rp.lucknow@rediffmail.com, sushmitasen.lkw@gmail.com
