From Yamabe to almost contact metric structure

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Abstract
The investigation of Yamabe solitons within almost contact metric manifolds has garnered significant interest recently, producing notable findings. This paper aims to explore the inverse problem: constructing almost contact metric structures on a three-dimensional Riemannian manifold endowed with an almost Yamabe soliton. Subsequently, we provide the techniques required to characterize the nature of these structures, accompanied by concrete examples.

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