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

Abstract

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.

Keywords

• Lorentzian para-Kenmotsu manifolds
• generalized symmetric metric connection of type (<i>α</i>, <i>β</i>)
• Einstein manifold
• projective curvature tensor