Characterization of Almost \(\eta\) -Ricci Solitons With Respect to Schouten-van Kampen Connection on Sasakian Manifolds
Tugba Mert *
Department of Mathematics, University of Sivas Cumhuriyet, 58140, Sivas, Turkey.
Mehmet Atceken
Department of Mathematics, University of Aksaray, 68100, Aksaray, Turkey.
Pakize Uygun
Department of Mathematics, University of Aksaray, 68100, Aksaray, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we investigate Sasakian manifolds that admit almost \(\eta\) -Ricci solitons with respect to the Schouten-van Kampen connection using certain curvature tensors. Concepts of Ricci pseudosymmetry for Sasakian manifolds admitting \(\eta\)-Ricci solitons are introduced based on the selection of specific curvature tensors such as Riemann, concircular, projective, pseudo-projective, M-projective, and W2 tensors. Subsequently, necessary conditions are established for a Sasakian manifold admitting \(\eta\)-Ricci soliton with respect to the Schouten-van Kampen connection to be Ricci semisymmetric, based on the choice of curvature tensors. Characterizations are then derived, and classifications are made under certain conditions.
Keywords: Ricci-pseudosymmetric manifold, \(\eta\)-Ricci soliton, Schouten-van Kampen connection