## Abstract

In this paper, we work on some properties of generalized quasi-Einstein and pseudo Ricci symmetric generalized quasi-Einstein manifolds. Firstly, some basic concepts about generalized quasi-Einstein manifolds are given. In the second section, the holonomy theory in 4-dimensional manifolds admitting a metric g is investigated and the holonomy algebras on these manifolds are determined. Then, we examine the existence of some vector fields on pseudo Ricci symmetric generalized quasi-Einstein manifolds and we prove some theorems. In the last section, as a special generalized quasi-Einstein space-time, pseudo Ricci symmetric generalized quasi-Einstein space-time is studied and some properties of it are obtained.

Original language | English |
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Pages (from-to) | 89-102 |

Number of pages | 14 |

Journal | Bulletin of the Iranian Mathematical Society |

Volume | 45 |

Issue number | 1 |

DOIs | |

Publication status | Published - 7 Feb 2019 |

### Bibliographical note

Publisher Copyright:© 2018, Iranian Mathematical Society.

### Funding

Acknowledgements The authors are thankful to the reviewer for his/her careful reading of the paper and valuable comments. One of the authors (BK) thanks The Scientific and Technological Research Council of Turkey (TÜB˙TAK) for financial support. She also expresses her sincere thanks to Professor Graham Hall for many useful discussions during her research at the University of Aberdeen.

Funders | Funder number |
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Türkiye Bilimsel ve Teknolojik Araştirma Kurumu |

## Keywords

- Generalized quasi-Einstein manifold
- Holonomy
- Pseudo Ricci symmetric manifold
- Vector field