On Quasistatistical F-Connections on the Anti-Kähler Manifolds

The paper focuses on investigating a specific type of quasistatistical F-connections within the context of an anti-K & auml;hler manifold. Initially, the paper establishes a connection between the Riemannian connection and the specialized quasistatistical F-connection. Following the establishment of this connection, the paper examines the forms of the curvature tensor, the Ricci curvature tensor, and the scalar curvature for the connection. It also explores the specific conditions under which the torsion tensor and curvature tensor fields associated with the quasistatistical F-connection exhibit holomorphic properties. Furthermore, the paper examines U(Ric)-vector fields with respect to these connections and delivers relevant outcomes associated with them. This analysis provides valuable insights into the behavior and properties of U(Ric)-vector fields within the considered framework. Finally, a concrete example on an anti-K & auml;hler-Walker manifold is presented, showing that the holomorphy conditions reduce to partial differential equations and that a harmonic potential on the parallel null distribution induces an explicitly computable quasistatistical F-connection.