This paper investigates $3$-dimensional generalized trans-Sasakian manifolds admitting generalized η-Ricci solitons. We establish necessary and sufficient conditions for the existence of such solitons and provide a complete characterization in the three-dimensional case. The obtained results clarify the interplay between the soliton equation and the underlying almost contact metric manifold. Explicit and concrete examples are presented to illustrate these results.
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Beldjilali et al. (2026) studied this question.
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