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 |
|---|---|
| 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 |
|---|---|
| Türkiye Bilimsel ve Teknolojik Araştirma Kurumu |
Keywords
- Generalized quasi-Einstein manifold
- Holonomy
- Pseudo Ricci symmetric manifold
- Vector field