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The goal of this paper is to study conformal Yamabe soliton and $*$-Yamabesoliton, whose potential vector field is torse forming. Here, we havecharacterized conformal Yamabe soliton admitting potential vector field astorse forming with respect to Riemannian connection, semi-symmetric metricconnection and projective semi-symmetric connection on Riemannian manifold. Wehave also shown the nature of $*$-Yamabe soliton with torse forming vectorfield on Riemannian manifold admitting Riemannian connection. Lastly we havedeveloped an example to corroborate some theorems regarding Riemannianconnection on Riemannian manifold.

Conformal Yamabe soliton and $*$-Yamabe soliton with torse forming potential vector field