Characterizations of ρ-Einstein solitons on LP-Sasakian manifolds admitting the Zamkovoy connection

Abstract

 The purpose of this research is to investigate ρ-Einstein solitons on LP-Sasakian manifolds under certain curvature conditions. The novelty of our research lies in the fact that we characterize ρ-Einstein solitons on LP-Sasakian manifolds equipped with the Zamkovoy connection when the structure vector field is considered as the potential vector field. We obtain some significant results on classifications of ρ-Einstein solitons in regard to the W₈-curvature tensor and the Zamkovoy connection. In extension, we build a non-trivial example of a three dimensional LP-Sasakian manifold endowed with the Zamkovoy connection.