关键词: Einstein-Weyl manifold, conformal mapping, generalized concircular mapping, isotropic manifold

Abstract:

In this article, after giving a necessary and sufficient condition for two Einstein-Weyl manifolds to be in conformal correspondence, we prove that any conformal mapping between such manifolds is generalized concircular if and only if the covector  field of the conformal mapping is locally a
gradient. Using this fact we deduce that any conformal mapping between two isotropic Weyl manifolds is a generalized concircular mapping. Moreover, it is shown that a generalized concircularly flat Weyl manifold is generalized concircular to an Einstein manifold and that its scalar curvature is prolonged covariant constant.

Key words: Einstein-Weyl manifold, conformal mapping, generalized concircular mapping, isotropic manifold