On LP-Kenmotsu Manifold with Regard to Generalized Symmetric Metric Connection of Type (α, β)

In the current article, we examine Lorentzian para-Kenmotsu (shortly, LP-Kenmotsu) manifolds with regard to the generalized symmetric metric connection (Formula presented.) of type (Formula presented.). First, we obtain the expressions for curvature tensor, Ricci tensor and scalar curvature of an LP-Kenmotsu manifold with regard to the connection (Formula presented.). Next, we analyze LP-Kenmotsu manifolds equipped with the connection (Formula presented.) that are locally symmetric, Ricci semi-symmetric, and (Formula presented.) -Ricci symmetric and also demonstrated that in all these situations the manifold is an Einstein one with regard to the connection (Formula presented.). Moreover, we obtain some conclusions about projectively flat, projectively semi-symmetric and (Formula presented.) -projectively flat LP-Kenmotsu manifolds concerning the connection (Formula presented.) along with several consequences through corollaries. Ultimately, we provide a 5-dimensional LP-Kenmotsu manifold example to validate the derived expressions.