On conformally recurrent Kahlerian Weyl spaces

Abstract

We consider a conformally recurrent Kahlerian Weyl space on which some pure and hybrid tensors are defined. We define the tensor G ij of weight {0} by G ij = H ij − H ji , where H ij is a tensor of weight {0} which can be written in terms of the covariant curvature tensor R ij kl and an antisymmetric tensor F kl by H ij = 1/2R ij kl F kl . It is shown that a Kahlerian Weyl space is an EinsteinWeyl space if and only if the tensor G ij is proportional to the tensor F ij . We also prove that the conformal recurrency of Kahlerian Weyl space implies its recurrency.