DOI: 10.36890/iejg.1894714 ISSN: 1307-5624

Generalized $\eta$-Ricci Soliton on 3-Dimensional Generalized Trans-Sasakian Manifolds

Beldjilali Gherici, Bouzir Habib, Bayour Benaoumeur
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This paper investigates $3$-dimensional generalized trans-Sasakian manifolds admitting generalized $\eta$-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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