Study of W9: Curvature Tensors on Lorentzian Para- Kenmotsu Manifolds

Abstract

This paper presents a study of the W9

-curvature tensor on Lorentzian Para-Kenmotsu manifolds, expanding

upon existing research to explore areas including W9

flatness, ξ − W9

flatness, φ − W9

flatness, and W9 - semi-symmetric on LP-Kenmotsu manifolds. Lorentzian Para-Kenmotsu manifolds satisfying the conditions;

Q. W9 = 0, W9

. Q = 0, R. W9 = 0, and W9 . W9 = 0.

The findings enhance knowledge of the geometric properties of these manifolds and offer fresh insights into the behavior of the W9

-curvature tensor within this context.

Keywords: Para-contact metric manifold, Lorentzian almost paracontact manifold, Lorentzian Para- Kenmotsu manifold, Einstein manifold, η −Einstein manifold, W9

-curvature tensor, W9 flat, ξ − W9 flat,

φ − W9 flat, and W9 -semi-symmetric.