Geometry of α-Cosymplectic Metric as *-Conformal η-Ricci-Yamabe Solitons Admitting Quarter-Symmetric Metric Connection

The outline of this research article is to initiate the development of a *-conformal eta-Ricci-Yamabe soliton in alpha-Cosymplectic manifolds according to the quarter-symmetric metric connection. Here, we have established some curvature properties of alpha-Cosymplectic manifolds in regard to the quarter-symmetric metric connection. Further, the attributes of the soliton when the manifold gratifies a quarter-symmetric metric connection have been displayed in this article. Later, we picked up the Laplace equation from *-conformal eta-Ricci-Yamabe soliton equation when the potential vector field xi of the soliton is of gradient type, admitting quarter-symmetric metric connection. Next, we evolved the nature of the soliton when the vector field's conformal killing reveals a quarter-symmetric metric connection. We show an example of a 5-dimensional alpha-cosymplectic metric as a *-conformal eta-Ricci-Yamabe soliton acknowledges quarter-symmetric metric connection to prove our results.