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 r...

1. Statement of Problem.-Many problems in plane potential theory can be solved easily, if one knows how to map the interior (or exterior) of a given closed curve C in the z-plane, conformally and one-one onto the interior (or exterior) of the unit circle t = e"' in the t-plane. This can be done by tabulated functions in some cases, but even in such cases, the solution often involves one or more...