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Ricci solitons and gradient Ricci solitons on 3-dimensional normal almost contact metric manifolds
U C DE, A DE
Published in KOSSUTH LAJOS TUDOMANYEGYETEM
2012
Volume: 80

Issue: 43467
Pages: 127 - 142
Abstract
The object of the present paper is to study a 3-dimensional normal almost contact metric manifold admitting Ricci solitons and gradient Ricci solitons. At first we give an example of a 3-dimensional normal almost contact metric manifold with α,β = constant. We prove that a 3-dimensional normal almost contact metric manifold admitting a Ricci soliton with a potential vector field V collinear with the characteristic vector field ε, is η-Einstein provided α,β = constant. Also we show that an η-Einstein 3-dimensional normal almost contact metric manifold with α,β = constant and V = ε admits a Ricci soliton. Finally we prove that if in a 3-dimensional normal almost contact metric manifold with constant scalar curvature, g is a gradient Ricci soliton, then the manifold is either α-Kenmotsu or an Einstein manifold provided α,β = constant.