  The goal of this paper is to study conformal Yamabe soliton and $*$-Yamabe
soliton, whose potential vector field is torse forming. Here, we have
characterized conformal Yamabe soliton admitting potential vector field as
torse forming with respect to Riemannian connection, semi-symmetric metric
connection and projective semi-symmetric connection on Riemannian manifold. We
have also shown the nature of $*$-Yamabe soliton with torse forming vector
field on Riemannian manifold admitting Riemannian connection. Lastly we have
developed an example to corroborate some theorems regarding Riemannian
connection on Riemannian manifold.

Differential Geometry