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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 54 Issue: 3

$\star$-Ricci-Yamabe solitons on almost coKähler manifolds

U.c. De(University of Calcutta)0000-0002-8990-4609
Adara M. Blaga(West University of Timisoara)0000-0003-0237-3866
Avijit Sarkar(University of Kalyani)0000-0002-7370-1698
Tarak Mandal(University of Kalyani)0000-0003-4808-8454
Pages
—
Publication Date
2025-06-24
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⚡ TL;DR(Too Long; Didn't Read)

It is proved that a compact almost coKähler manifold admitting a $\star$-Ricci--Yamabe soliton under certain restriction on $\star$-scalar curvature is coKähler and $\star$-Ricci flat; in addition, that the soliton is steady. $(\kappa, \mu)$-almost coKähler manifolds admitting such solitons are also considered and finally, the obtained results are completed by non-trivial examples.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The aim of the present article is to analyze $\star$-Ricci--Yamabe solitons on almost coKähler manifolds and to characterize them when the potential vector field is pointwise collinear with the Reeb vector field.
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Key Findings & Data:The aim of the present article is to analyze $\star$-Ricci--Yamabe solitons on almost coKähler manifolds and to characterize them when the potential vector field is pointwise collinear with the Reeb vector field.
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Conclusion & Impact:It is proved that a compact almost coKähler manifold admitting a $\star$-Ricci--Yamabe soliton under certain restriction on $\star$-scalar curvature is coKähler and $\star$-Ricci flat; in addition, that the soliton is steady. $(\kappa, \mu)$-almost coKähler manifolds admitting such solitons are also considered and finally, the obtained results are completed by non-trivial examples.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:almost coKähler manifold · $(\kappa$ · $\mu)$-nullity distribution

Abstract

The aim of the present article is to analyze $\star$-Ricci--Yamabe solitons on almost coKähler manifolds and to characterize them when the potential vector field is pointwise collinear with the Reeb vector field. It is proved that a compact almost coKähler manifold admitting a $\star$-Ricci--Yamabe soliton under certain restriction on $\star$-scalar curvature is coKähler and $\star$-Ricci flat; in addition, that the soliton is steady. $(\kappa, \mu)$-almost coKähler manifolds admitting such solitons are also considered and finally, the obtained results are completed by non-trivial examples.

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Cite This Article

De, U., Blaga, A. M., Sarkar, A., Mandal, T. (2025). $\star$-Ricci-Yamabe solitons on almost coKähler manifolds. Hacettepe Journal of Mathematics and Statistics, Volume: 54 Issue: 3. https://doi.org/10.15672/hujms.1357924

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