Some Properties of RICCI Solitons in LP-Kenmotsu Manifolds

Abstract

Examining Ricci solitons in Lorentzian para-Kenmotsu manifolds is the goal of this paper. We have established that a symmetric parallel second-order covariant tensor in a Lorentzian para-Kenmotsu manifold is a constant multiple of the metric tensor. We have shown that if L_V g+2S is parallel to the Levi-Civita connection associated with g, where V is a given vector field, then (g,V,λ) is a Ricci soliton. We have observed that a Ricci soliton in a W_2-semi-symmetric Lorentzian para-Kenmotsu manifold is shrinking. Furthermore, certain curvature properties of Lorentzian para-Kenmotsu manifolds admitting Ricci solitons are studied. Finally, we have provided an example of a 3-dimensional Lorentzian para-Kenmotsu manifold.