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Sasakian 3-manifolds admitting a gradient Ricci-Yamabe soliton

Dibakar Dey
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2021.09|한국수학논문집 (Korean Journal of Mathematics)|제29권 제3호|pp. 547-554

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키워드

Sasakian 3-manifoldRicci-Yamabe solitonGradient Ricci-Yamabe solitonInfinitesimal automorphism.
주제분류수학

초록

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.

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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