Cotton tensor on Sasakian 3-manifolds admitting eta-Ricci solitons

Year 2021, Volume: 70 Issue: 2, 569 - 581, 31.12.2021

Debabrata Kar Pradip Majhi

https://doi.org/10.31801/cfsuasmas.769405

Abstract

The object of the present paper is to characterize Cotton tensor on a 3-dimensional Sasakian manifold admitting $\eta$-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 $\eta$-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.

Keywords

Einstein manifold, Ricci soliton, $\eta$-Ricci soliton, Cotton tensor, Sasakian manifold

Supporting Institution

Council of Scientific and Industrial Research, India

Project Number

File no : 09/028(1007)/2017-EMR-1)

Thanks

The author Debabrata Kar is supported by the Council of Scientific and Industrial Research, India

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