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In this paper, left-invariant almost contact metric structures onthree-dimensional non-unimodular Lie groups are investigated. It is proved thatfor every Riemannian Lie group, there is one of these structures. In addition,left-invariant normal almost contact metric structures on three dimensionalnon-unimodular Lie groups are classified.

Classification of almost contact metric structures on three-dimensional non-unimodular Lie groups