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

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.


Keywords


Sasakian 3-manifold; Ricci-Yamabe soliton; Gradient Ricci-Yamabe soliton; Infinitesimal automorphism.

Subject classification

53C25; 35Q51

Sponsor(s)



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