## 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 be- tween 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_{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.

Original language | English |
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Pages (from-to) | 463-475 |

Number of pages | 13 |

Journal | Bulletin of the Iranian Mathematical Society |

Volume | 41 |

Issue number | 2 |

Publication status | Published - 1 Apr 2015 |

### Bibliographical note

Publisher Copyright:© 2015 Iranian Mathematical Society.

## Keywords

- Conformal mapping
- Einstein tensor
- Flat Weyl manifold
- Isotropic Weyl manifold
- Weyl manifold