The Generalized Symmetric Non-Metric Connection and Its Applications to ∗-Conformal η-Ricci–Yamabe Solitons on α-Cosymplectic Manifolds

This paper investigates the geometric properties of ∗-conformal η-Ricci–Yamabe solitons (∗-conformal η-RYS) on α-cosymplectic manifolds (α−CSM) equipped with a newly introduced connection known as the generalized symmetric non-metric connection (GSNMC). The existence of this connection is rigorously established, and a thorough analysis is conducted on various curvature characteristics of α−CSM manifolds in the context of the GSNMC. This paper further explores the behavior, classification, and properties of ∗-conformal η-RYS, including their applications in different geometric settings. A particular focus is placed on the harmonic interpretation of ∗-conformal η-RYS associated with the GSNMC on α−CSM. To substantiate the theoretical developments, an explicit example is provided: a five-dimensional α-cosymplectic metric is constructed that incorporates a ∗-conformal η-RYS structure with respect to the proposed connection. This example serves to illustrate the practical applicability of the results and validates the theoretical framework presented in the paper.