IMPACT OF GRADIENT SOLITONS ON PERFECT FLUID SPACETIMES ADMITTING A TYPE OF SEMI-SYMMETRIC NON-METRIC CONNECTION

Abstract

This article carries out the investigation of a 4-dimensional Lorentzian manifold M^4 endowed with a type of semi-symmetric non-metric connection (SSNMC) whose associated vector field is parallel with respect to the semi-Riemannian connection. We investigate gradient Ricci solitons, gradient η-Ricci solitons and gradient Yamabe soliton with respect to SSNMC and we obtain several interesting results on perfect fluid spacetimes.