Characterization of Almost \(\eta\) -Ricci Solitons With Respect to Schouten-van Kampen Connection on Sasakian Manifolds

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.