On conformally recurrent Kahlerian Weyl spaces

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