Cotton tensor on Sasakian 3-manifolds admitting eta-Ricci solitons
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Date
2021
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Publisher
Ankara Üniversitesi
Abstract
The object of the present paper is to characterize Cotton tensor on a 3-dimensional Sasakian manifold admitting
η
-Ricci solitons. After introduction, we study 3-dimensional Sasakian manifolds and introduce a new notion, namely, Cotton pseudo-symmetric manifolds. Next we deal with the study Cotton tensor on a Sasakian 3-manifold admitting
η
-Ricci solitons. Among others we prove that such a manifold is a manifold of constant scalar curvature and Einstein manifold with some appropriate conditions. Also, we classify the nature of the soliton metric. Finally, we give an important remark.
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Keywords
Einstein manifold, Ricci soliton, η -Ricci soliton, Cotton tensor, Sasakian manifold