Linearly independent curvature tensors of half-symmetric affine connection

In this paper, a half-symmetric affine connection is considered. Based on this connection, the corresponding linearly independent curvature tensors are determined. Subsequently, a special half-symmetric affine connection (K. Yano, 1965) is examined. First, the dual and symmetric connections of this special half-symmetric connection are defined. Then, a necessary and sufficient condition for the torsion vanishing of the special half-symmetric affine connection is determined. Linearly independent curvature tensors of the special half-symmetric affine connection are then identified. Finally, necessary and sufficient conditions under which the dual and symmetric connections of the special half-symmetric affine connection are F-connections are established.