$k$-Yamabe and quasi $k$-Yamabe solitons on imperfect fluid generalized Robertson — Walker spacetime

In this research article, we estimate the behavior of an imperfect fluid generalized Robertson — Walker spacetime ($GRW$) in terms of $k$-Yamabe soliton with torseforming vector field. Besides this, we evaluate a specific situation when the potential vector filed $\xi$ is of the form of gradient i.e., $\xi = \mathrm{grad}\,(\Psi)$, we extract a Laplace — Poisson equation, and Liouville equation from the quasi $k$-Yamabe soliton equation.