Pseudosymmetric Characterizations for Sasakian Manifolds Admitting General Connection

In this study, the geometry of Sasakian manifolds is investigated using a general connection instead of the classical Levi-Civita connection. On a Sasakian manifold admitting a general connection, we first define the projective and concircular curvature tensors and obtain the characterizations of projectively flat, concircularly flat, projectively semi-symmetric, and concircularly semi-symmetric Sasakian manifolds. Additionally, by discuss the act of projective and concircular curvature tensors on each other, we reveal the properties of Sasakian manifolds admitting a general connection. In the next section, we construct Ricci-Bourguignon solitons on Sasakian manifolds admitting a general connection. In this connection, we search Ricci pseudo-symmetric, projectively Ricci pseudo-symmetric, and concircularly Ricci pseudo-symmetric Sasakian manifolds admitting Ricci-Bourguignon solitons. Consequently, we compare all these important properties on Sasakian manifolds separately according to the Tanaka-Webster, Schouten-van Kampen, and Zamkovoy connections.