Korean J. Math. Vol. 29 No. 3 (2021) pp.547-554
DOI: https://doi.org/10.11568/kjm.2021.29.3.547

Sasakian 3-manifolds admitting a gradient Ricci-Yamabe soliton

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Dibakar Dey

Abstract

The object of the present paper is to characterize Sasakian 3-manifolds admitting a gradient Ricci-Yamabe soliton. It is shown that a Sasakian 3-manifold $M$ with constant scalar curvature admitting a proper gradient Ricci-Yamabe soliton is Einstein and locally isometric to a unit sphere. Also, the potential vector field is an infinitesimal automorphism of the contact metric structure. In addition, if $M$ is complete, then it is compact.



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