On anti-Kähler manifolds with complex semi-symmetric metric F-connection

Abstract

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