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