CONFORMAL MAPPINGS PRESERVING EINSTEIN TENSOR OF WEYL MANIFOLDS


Guerlek M., Civi G.

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol.41, no.2, pp.463-475, 2015 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 2
  • Publication Date: 2015
  • Title of Journal : BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.463-475

Abstract

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 (W) over tilde (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.