η-Ricci-Yamabe Solitons on Sasakian Manifolds Admitting Non-Levi-Civita Connections

In this paper, we study η-Ricci–Yamabe solitons on Sasakian manifolds by employing a general affine connection instead of the Levi-Civita connection. We focus on Sasakian manifolds admitting η-Ricci solitons with respect to a general connection under the assumptions of Ricci pseudosymmetry and Ricci semisymmetry. Within this setting, we obtain explicit characterization results for Ricci pseudosymmetric and Ricci semisymmetric Sasakian manifolds associated with several important types of connections, namely the quarter-symmetric connection, the Schouten–Van Kampen connection, the Tanaka–Webster connection, and the Zamkovoy connection. Furthermore, we derive necessary and sufficient‘ conditions for the existence of η-Ricci soliton, η-Yamabe soliton, and η-Einstein soliton structures on Sasakian manifolds equipped with a general connection. Our results generalize and unify various known characterizations in Sasakian geometry and demonstrate how different geometric soliton structures behave under a broader class of affine connections.