Journals / Konuralp Journal of Mathematics / 2026 / Volume: 14 Issue: 1

$\eta $-Ricci-Bourguignon Solitons on Three-Dimensional H-Paracontact Metric Manifolds

İrem Küpeli Erken(Bursa Technical University)0000-0003-4471-3291
Berna Özdamar(BURSA TECHNICAL UNIVERSITY)0009-0008-7764-9314
Pages
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Publication Date
2026-04-30
DOI
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Furthermore, we present examples that provide our results.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we investigate $\eta$-Ricci-Bourguignon solitons and gradient $\eta$-Ricci-Bourguignon solitons on $3$-dimensional $H$% -paracontact metric manifolds and characterize them based on the forms the operator $h$ can take.
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Key Findings & Data:In this paper, we investigate $\eta$-Ricci-Bourguignon solitons and gradient $\eta$-Ricci-Bourguignon solitons on $3$-dimensional $H$% -paracontact metric manifolds and characterize them based on the forms the operator $h$ can take.
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Conclusion & Impact:Furthermore, we present examples that provide our results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Paracontact Metric Manifolds · Paracontact (κ · μ)-Manifolds

Abstract

In this paper, we investigate $\eta$-Ricci-Bourguignon solitons and gradient $\eta$-Ricci-Bourguignon solitons on $3$-dimensional $H$% -paracontact metric manifolds and characterize them based on the forms the operator $h$ can take. Furthermore, we present examples that provide our results.

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Cite This Article

Erken, İ. K., Özdamar, B. (2026). $\eta $-Ricci-Bourguignon Solitons on Three-Dimensional H-Paracontact Metric Manifolds. Konuralp Journal of Mathematics, Volume: 14 Issue: 1. https://ajindex.com/articles/1521444

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References (22)

  1. Blaga,A.,Ozgur,C.,Remarks on submanifolds as almost h-Ricci Bourguignon solitons. Facta Universitatis Ser. Math. Inform. 37(2), 397–407, (2022)
  2. Blaga,A. M.,Tastan,H.M.,Some results on almosth-Ricci-Bourguignon solitons. J. Geom. Phys. 168, Article ID 104316.(2021)
  3. Bourguignon,J. P.,Ricci curvature and Einstein metrics in: Global Differential Geometry and Global Analysis, Lecture Notes in Mathematics. 838, 42–63, (1981)
  4. Calvaruso,C.,Perrone, D.,Geometry of H -paracontact metric manifolds. Publ. Math. Debrecen, 86/3-4, 325–346, (2015)
  5. Cappelletti Montano,B.,K¨upeli Erken, ˙I.,Murathan, C., Nullity conditions in paracontact geometry. Differential Geom. Appl., 30, 665–693, (2012)
  6. Catino,G.,Cremaschi,L.,Djadli,Z.,Mantegazza,C., Mazzieri,L., The Ricci-Bourguignon flow, Pac. J. Math. 287, 337–370, (2017)
  7. Catino,G., Mazzieri,L.Gradient Einstein solitons. Nonlinear Analysis. 132, 66–94, (2016)
  8. Cho,J. T., Almost contact 3-manifolds and Ricci solitons. Int. J. Geom. Methods Mod. Phys. 10(01), 1220022, (2013). https://doi.org/10.1142/ S0219887812200228
  9. De,U. C., Turan,M.,Yildiz, A. and De,A.Ricci solitons and gradient Ricci solitons on 3-dimensional normal almost contact metric manifolds.Publ. Math. Debrecen 80(1-2), 127–142, (2012)
  10. Dwivedi,S., Some results on Ricci-Bourguignon solitons and almost solitons. Can. Math. Bull. 64, 591–604, (2021)
  11. Ghosh,A.,Kenmotsu 3-metric as a Ricci soliton. Chaos Solitons Fractals 44(8), 647–650, (2011)
  12. Hamilton,R. S.,Three-manifolds with positive Ricci curvature. J. Differ. Geom. 17 (2), 255–306, (1982)
  13. Hamilton,R. S. The Ricci flow on surfaces, Contemp. Math. 71, 237–262, (1988)
  14. Khatri,M., Singh,J.P. Ricci-Bourguignon Soliton on Three-Dimensional Contact Metric Manifolds, Mediterr. J. Math. 21, 70, (2024)
  15. Kupeli Erken,I.,Murathan,C.,A study of three-dimensional paracontact (k˜;m˜;n˜ )-spaces, Int. J. Geom. Methods Mod. Phys., 14, (7), (2017)
  16. I.Kupeli Erken, Generalized (k˜ 6= 􀀀1;m˜ )-Paracontact metric manifolds with x (m˜ ) = 0, Int. Electron. J. Geom., 8(1), 77–93, (2015)
  17. Mandal,T., De, UC., Sarkar,A., h -Ricci-Bourguignon solitons on three-dimensional (almost) coK¨ahler manifolds, Math Method Appl Sci., 1-14, (2024)
  18. Shaikh,A.A.,Cunha,A.W.,Mandal,P.,Some characterizations of r-Einstein solitons, J. Geom. Phys. 166, 104270, (2021)
  19. Shaikh,A.A.,Mondal, C.K.,Mandal,P. Compact gradient r-Einstein soliton is isometric to the Euclidean sphere.Indian J. Pure Appl. Math. 52, 335–339, (2021)
  20. Zamkovoy,S., Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom., 36(1), 37–60, (2009)
  21. Zamkovoy,S.,Tzanov,V., Non-existence of flat paracontact metric structures in dimension greater than or equal to five. Annuaire Univ. Sofia Fac. Math. Inform., 100, 27–34, (2009)
  22. Kupeli Erken,I.,Murathan,C.,A study of three-dimensional paracontact (k˜;m˜;n˜ )-spaces, Int. J. Geom. Methods Mod. Phys., 14, (7), (2017)