On conformally recurrent Kahlerian Weyl spaces

Abstract

From the abstract: We consider a conformally recurrent Kählerian 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 \(R_{ijk\ell}\) and an antisymmetric tensor \(F^{k\ell}\) by \(H_{ij}=1/2R_{ijk\ell}F^{k\ell}\). It is shown that a Kählerian Weyl tensor space is an Einstein-Weyl space if and only if the tensor \(G_{ij}\) is proportional to the tensor \(F_{ij}\).