@article {
author = {Gürlek, M. and Çivi, G.},
title = {Conformal mappings preserving the Einstein tensor of Weyl manifolds},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {41},
number = {2},
pages = {463-475},
year = {2015},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
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 $\tilde{W}_n$, 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.},
keywords = {Weyl manifold,Einstein tensor,conformal mapping,flat Weyl manifold,isotropic Weyl manifold},
url = {http://bims.iranjournals.ir/article_623.html},
eprint = {http://bims.iranjournals.ir/article_623_d097ee44c57dfd39ee745fc63874c1bf.pdf}
}