*-η-Ricci-Yamabe Solitons on α-Cosymplectic Manifolds with a Quarter-Symmetric Metric Connection
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In this paper, we study *-η-Ricci-Yamabe solitons on α-cosymplectic manifolds with respect to a quarter-symmetric metric connection. We establish several curvature properties of such manifolds and examine the behavior of solitons under this connection. When the potential vector field ξ is of gradient type, we derive a Laplace equation from the *-η-Ricci-Yamabe soliton equation. We also analyze the nature of the soliton in this context. Finally, we provide an explicit example of a 5-dimensional α-cosymplectic manifold admitting a *-η-Ricci-Yamabe soliton with respect to a quarter-symmetric metric connection to support our theoretical results.
Abstract
In this paper, we study *-η-Ricci-Yamabe solitons on α-cosymplectic manifolds with respect to a quarter-symmetric metric connection. We establish several curvature properties of such manifolds and examine the behavior of solitons under this connection. When the potential vector field ξ is of gradient type, we derive a Laplace equation from the *-η-Ricci-Yamabe soliton equation. We also analyze the nature of the soliton in this context. Finally, we provide an explicit example of a 5-dimensional α-cosymplectic manifold admitting a *-η-Ricci-Yamabe soliton with respect to a quarter-symmetric metric connection to support our theoretical results.