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

Authors : Debabrata KAR, Pradip MAJHİ

Pages : 569-581

Doi:10.31801/cfsuasmas.769405

View : 13 | Download : 6

Publication Date : 2021-12-31

Article Type : Research Paper

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