Study Of Some Curvature Tensors On Lorentzian Para-Kenmotsu Manifolds

Abstract

A comprehensive analysis of curvature tensors on Lorentzian Para Kenmotsu manifolds focusing on W3, W5 and W9 curvature tensors was done. The properties of these curvature tensors under various conditions on these manifolds were explored and examined as well as their geometric implications. The study also included investigations of W3-flat, W5 -flat and W9-flat Lorentzian Para Kenmotsu manifolds and their connections to η-Einstein, Einstein and special η-Einstein properties. Additionally, analysis of the Ricci operator’s behaviors on Lorentzian Para Kenmotsu manifolds under the conditions W3 · Q = 0, W5 · Q = 0, W9 · Q = 0 was conducted. Expressions for these curvature tensors while considering the condition Wi (ξX) · Wi = 0, where i=3, 5, 9 were derived. Proves to determine whether these manifolds are flat were provided. The findings of these studies enhance our understanding of the geometric properties of Lorentzian Para Kenmotsu manifolds in relation to Wi-curvature tensors.