TY - JOUR
ID - 623
TI - Conformal mappings preserving the Einstein tensor of Weyl manifolds
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Gürlek, M.
AU - Çivi, G.
AD - Istanbul Technical university
Maslak
AD - Istanbul technical university
Faculty of Science and letters, dept . of Math., maslak
Y1 - 2015
PY - 2015
VL - 41
IS - 2
SP - 463
EP - 475
KW - Weyl manifold
KW - Einstein tensor
KW - conformal mapping
KW - flat Weyl manifold
KW - isotropic Weyl manifold
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_623.html
L1 - http://bims.iranjournals.ir/article_623_d097ee44c57dfd39ee745fc63874c1bf.pdf
ER -