Applications of a Special Generalized Quasi-Einstein Manifold
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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.
KeywordsGeneralized quasi-Einstein manifold Holonomy Pseudo Ricci symmetric manifold Vector field
Mathematics Subject ClassificationPrimary 53B20 Secondary 53C25 53C29
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.