η-Ricci-Yamabe Solitons on Sasakian Manifolds Admitting Non-Levi-Civita Connections
Tugba Mert *
Department of Mathematics, Faculty of Science, University of Sivas Cumhuriyet, 58140, Sivas, Turkey.
Mehmet Atceken
Department of Mathematics, Faculty of Art and Science, University of Aksaray, 68100, Aksaray, Turkey.
Mohd Danish Siddiqi
Department of Mathematics College of Science, Jazan University, P.O. Box 277, Jazan 45142, Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
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.