A Conformal η-Ricci Soliton on a Four-Dimensional Lorentzian Para-Sasakian Manifold

Abstract

This paper focuses on some geometrical and physical properties of a conformal η-Ricci soliton (Cη-RS) on a four-dimension Lorentzian Para-Sasakian (LP-S) manifold. The first section presents an introduction to Cη-RS on LP-S manifolds, followed by a discussion of preliminary ideas about the LP-Sasakian manifold. In the subsequent sections, we establish several results pertaining to four-dimension LP-S manifolds that exhibit Cη-RS. Additionally, we consider certain conditions associated with Cη-RS on four-dimension LP-S manifolds. Besides these geometrical points of view, we consider this soliton in a perfect fluid spacetime and obtain some interesting physical properties. Finally, we present a case study of a Cη-RS on a four-dimension LP-S manifold.