Analysis of some properties of w5 curvature tensor in Lorentzian Para Kenmotsu Manifold

Abstract

This paper investigates the properties of W5 curvature tensors on Lorentzian Para Kenmotsu manifolds. Properties of this Curvature tensor under various conditions on these manifolds are explored and their geometric implications are examined. The study also includes investigations of W5 flatness, 𝜉 - 𝑊5 flatness, 𝜙 − 𝑊5 flatness and 𝑊5 -Semisymmetric on Lorentzian Para Kenmotsu manifolds and their connections to 𝜂-Einstein, Einstein and special 𝜂 -Einstein. Additionally, The Ricci operator's behaviors on Lorentzian Para Kenmotsu manifolds under the conditions 𝑊5.𝑄 = 0, 𝑄. 𝑊5 = 0 are analyzed. Expressions for this curvature tensor while considering the condition W5 (𝜉, 𝑋). W5 = 0, 𝑅. W5 = 0 and 𝑊5. 𝑊5 = 0 are derived. Proves to determine whether these manifolds are flat will be provided. The findings of this study enhance understanding of the geometric properties of Lorentzian Para Kenmotsu manifolds in relation to W5 curvature tensors.