conformal mappings preserving the einstein tensor of weyl manifolds

in this paper, we obtain a necessary and sufficient condition for a conformal mapping between two weyl manifolds to preserve einstein tensor. then we prove that some basic curvature tensors of $w_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. also, we obtained the relation between the scalar curvatures of the weyl manifolds related by a conformal mapping preserving the einstein tensor with a gradient covector field. then, we prove that a weyl manifold $w_n$ and a flat weyl manifold $tilde{w}_n$, which are in a conformal correspondence preserving the einstein tensor are einstein-weyl manifolds. moreover, we show that an isotropic weyl manifold is an einstein-weyl manifold with zero scalar curvature and we obtain that a weyl manifold $w_n$ and an isotropic weyl manifold related by the conformal mapping preserving the einstein tensor are einstein-weyl manifolds.