Study of W 𝐖�𝟑� - Curvature Tensor on Lorentzian Para-Kenmotsu Manifolds

Abstract

This study undertakes a comprehensive analysis of curvature tensors on Lorentzian Para Kenmotsu manifolds focusing on W3-Curvature tensor. Properties of this Curvature tensor under various conditions on these manifolds are explored and their geometric implications examined. The study also includes investigations of W3-flatness, (𝜉 - W3) flatness, (𝜙 − 𝑊3) flatness and 𝑊3 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 W3. 𝑄 = 0, 𝑄. 𝑊3 = 0 are analyzed. Expressions for this curvature tensor while considering the condition W3(𝜉, 𝑋). W3 = 0, 𝑅. W 3 = 0 and 𝑊3. 𝑊3 = 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 W3 curvature tensors