On Anti-Kähler manifolds with complex semi-symmetric metric $F-$connection

In this paper, we construct a complex semi-symmetric metric $F$-connection on an anti-Kähler manifold. First, we present some results concerning the torsion tensor of the complex semi-symmetric metric $F$-connection. Finally, we find expressions of the curvature tensor, the conharmonic curvature tensor and the Weyl projective curvature tensor of such connection, and study their properties.