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Applications of a Special Generalized Quasi-Einstein Manifold

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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.

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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 (TÜBİTAK) 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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Marmara University, Goztepe Campus, 34722, Istanbul, Turkey

    Bahar Kırık

  2. Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University, Maslak, 34469, Istanbul, Turkey

    Füsun Özen Zengin

Authors
  1. Bahar Kırık
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  2. Füsun Özen Zengin
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Correspondence to Bahar Kırık.

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Communicated by Eaman Eftekhary.

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Kırık, B., Özen Zengin, F. Applications of a Special Generalized Quasi-Einstein Manifold. Bull. Iran. Math. Soc. 45, 89–102 (2019). https://doi.org/10.1007/s41980-018-0121-y

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  • DOI: https://doi.org/10.1007/s41980-018-0121-y

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