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Journals / International Electronic Journal of Geometry / 2026 / Volume: 19 Issue: 2

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

Beldjilali Gherici(University of Mascara, Algeria.)0000-0002-8933-1548
Bouzir Habib(University of Mascara, Algeria.)0000-0002-6117-136X
Bayour Benaoumeur(University of Mascara, Algeria.)0000-0003-3504-4655
Pages
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Publication Date
2026-10-25
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Explicit and concrete examples are presented to illustrate these results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper investigates $3$-dimensional generalized trans-Sasakian manifolds admitting generalized $\eta$-Ricci solitons.
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Key Findings & Data:We establish necessary and sufficient conditions for the existence of such solitons and provide a complete characterization in the three-dimensional case.
💡
Conclusion & Impact:Explicit and concrete examples are presented to illustrate these results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Almost contact metric structure · trans-Sasakian manifolds · Ricci soliton

Abstract

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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Cite This Article

Gherici, B., Habib, B., Benaoumeur, B. (2026). Generalized $\eta$-Ricci Soliton on 3-Dimensional Generalized Trans-Sasakian Manifolds. International Electronic Journal of Geometry, Volume: 19 Issue: 2. https://doi.org/10.36890/iejg.1894714

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