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Istanbul technical university Faculty of Science and letters, dept . of Math., maslak
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.
Gürlek, M., & Çivi, G. (2015). Conformal mappings preserving the Einstein tensor of Weyl manifolds. Bulletin of the Iranian Mathematical Society, 41(2), 463-475.
MLA
M. Gürlek; G. Çivi. "Conformal mappings preserving the Einstein tensor of Weyl manifolds". Bulletin of the Iranian Mathematical Society, 41, 2, 2015, 463-475.
HARVARD
Gürlek, M., Çivi, G. (2015). 'Conformal mappings preserving the Einstein tensor of Weyl manifolds', Bulletin of the Iranian Mathematical Society, 41(2), pp. 463-475.
VANCOUVER
Gürlek, M., Çivi, G. Conformal mappings preserving the Einstein tensor of Weyl manifolds. Bulletin of the Iranian Mathematical Society, 2015; 41(2): 463-475.
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