SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2025 / Volume: 74 Issue: 4

$\eta$-Ricci-Bourguignon solitons on Kenmotsu manifolds with $\varphi(\mathcal{R}ic)$-vector fields

Moctar Traore(İSTANBUL ÜNİVERSİTESİ)0000-0003-2132-789X
Hakan Mete Taştan(ISTANBUL UNIVERSITY)0000-0002-0773-9305
Pages
—
Publication Date
2025-12-24
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

Finally, we prove that an $\eta$-Ricci-Bourguignon soliton on a hypersurface whose potential vector field is the tangential component of the $\varphi(\mathcal{R}ic)$-vector field is both a generalized and a pseudo-generalized quasi-Einstein manifold.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The present study concerns the investigation of Kenmotsu manifolds endowed with $\eta$-Ricci-Bourguignon solitons.
📊
Key Findings & Data:In particular, we aim to establish certain properties of $\eta$-Ricci-Bourguignon solitons on submanifolds isometrically immersed into a Kenmotsu manifold when its potential vector field is the tangential component of the $\varphi(\mathcal{R}ic)$-vector field.
💡
Conclusion & Impact:Finally, we prove that an $\eta$-Ricci-Bourguignon soliton on a hypersurface whose potential vector field is the tangential component of the $\varphi(\mathcal{R}ic)$-vector field is both a generalized and a pseudo-generalized quasi-Einstein manifold.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$\ast$-Ricci-Bourguignon solitons · $\eta$-Ricci-Bourguignon solitons · $\varphi(\mathcal{R}ic)$-vector field

Abstract

The present study concerns the investigation of Kenmotsu manifolds endowed with $\eta$-Ricci-Bourguignon solitons. In particular, we aim to establish certain properties of $\eta$-Ricci-Bourguignon solitons on submanifolds isometrically immersed into a Kenmotsu manifold when its potential vector field is the tangential component of the $\varphi(\mathcal{R}ic)$-vector field. Finally, we prove that an $\eta$-Ricci-Bourguignon soliton on a hypersurface whose potential vector field is the tangential component of the $\varphi(\mathcal{R}ic)$-vector field is both a generalized and a pseudo-generalized quasi-Einstein manifold.

🔖

Cite This Article

Traore, M., Taştan, H. M. (2025). $\eta$-Ricci-Bourguignon solitons on Kenmotsu manifolds with $\varphi(\mathcal{R}ic)$-vector fields. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 74 Issue: 4. https://doi.org/10.31801/cfsuasmas.1540817

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (35)

  1. Blaga, A. M., Taştan, H. M., Some results on almost $\eta$-Ricci-Bourguignon solitons, J. Geom. Phys., 168 (2021), 104316. https://doi.org/10.1016/j.geomphys.2021.104316.
  2. Blaga, A. M., Özgür, C., Almost $\eta$-Ricci and almost $\eta$-Yamabe solitons with torse-forming potential vector field, Quaest Math., 45(1) (2022), 143-163. https://doi.org/10.2989/16073606.2020.1850538.
  3. Blaga, A. M., Perktaş, S. Y., Remarks on almost $\eta$-Ricci solitons in $\epsilon$-para Sasakian manifolds, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat., 68(2) (2019), 1621-1628. https://doi.org/10.31801/cfsuasmas.546595.
  4. Blair, D. E., Riemannain Geometry of Contact and Symplectic Manifolds, Lecture Notes in Math. Springer Berlin, 1976.
  5. Bourguignon, J. P., Ricci curvature and Einstein metrics, in: Global Differential Geometry and Global Analysis: Proceedings of the Colloquium Held at the Technical University of Berlin, November 21–24, 1979. Berlin, Heidelberg: Springer Berlin Heidelberg, (2006), 42-63.
  6. Călin, C., Crasmareanu, M., Eta-Ricci solitons on Hopf hypersurfaces in complex space forms, Rev. Roumaine Math. Pures Appl., 57(1) (2012), 55–63.
  7. Catino, G., Cremaschi, L., Djadli, Z., Mantegazza, C., Mazzieri, L., The Ricci-Bourguignon flow, Pac. J. Math., 287(2) (2017), 337–370. https://doi.org/10.2140/pjm.2017.287.337.
  8. Chaki, M. C., Maity, R. K., On quasi Einstein manifolds, Publ. Math. Debrecen, 57(3-4) (2000), 297-306.
  9. Chen, B. Y., Geometry of Submanifolds, Dekker, New York, 1973.
  10. Chen, B. Y., Some results on concircular vector fields and their applications to Ricci solitons, Bull. Korean Math. Soc., 52(5) (2015), 1535-1547. http://dx.doi.org/10.4134/BKMS.2015.52.5.1535.
  11. Cho, J. T., Kimura, M., Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math.J., 61(2) (2009), 205–212. https://doi.org/10.2748/tmj/1245849443.
  12. De, U. C., Ghosh, G. C., On generalized quasi Einstein manifolds, Kyungpook Math J., 44(4) (2004), 607-15.
  13. Deszcz, R., Hotlos, M., Şentürk, Z., On curvature properties of quasi-Einstein hypersurfaces in semi-Euclidean space, Soochow J. Math., 27(4) (2004), 375-89.
  14. Dwivedi, S., Some results on Ricci-Bourguignon solitons and almost solitons, Can. Math. Bull., 64(3) (2021), 591–604. https://doi.org/10.4153/S0008439520000673.
  15. Fialkow, A., Conformal geodesics, Trans. Amer. Math. Soc., 45(3) (1939), 443-473. https://doi.org/10.2307/1990011.
  16. Gerdan Aydın, S., Traore, M., Taştan, H. M., $\zeta(Ric)$-vector fields on doubly warped product manifolds, Istanbul J. Math., 1(2) (2023), 67-73. https://doi.org/10.26650/ijmath.2023.00008.
  17. Ghosh, A., Patra, D. S., $\ast$-Ricci soliton within the frame-work of Sasakian and $(K, \mu)$-contact manifold, Int. J. Geom. Methods Mod. Phys., 15(7) (2018), 1850120. https://doi.org/10.1142/S0219887818501207.
  18. Hamilton, R. S., The Ricci flow on surfaces, Mathematics and general relativity, Contemp. Math., 71 (1988), 237-262. https://doi.org/10.1090/conm/071/954419.
  19. Heinterleitner, I., Kiosak, V. A., $\varphi$(Ric)-vector fields in Riemannian spaces, Arch. Math., 44(5) (2008), 385–390. http://dml.cz/dmlcz/127124.
  20. Heinterleitner, I., Kiosak, V. A., $\varphi$(Ric)-vector fields on conformally flat spaces, AIP. Conf. Prof, 1191(1) (2009), 98-103. https://doi.org/10.1063/1.3275604.
  21. Kaimakamis, G., Panagiotidou, K., $\ast$-Ricci solitons of real hypersurfaces in non-flat complex space forms, J. Geom. Phys, 86(2014), 408-413. https://doi.org/10.1016/j.geomphys.2014.09.004.
  22. Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J, 24(1) (1972), 93-103. https://doi.org/10.2748/tmj/1178241594.
  23. Kırık, B., Özen Zengin, F., Conformal mappings of quasi-Einstein manifolds admitting special vector fields, Filomat, 29(3) (2015), 525–534. https://doi.org/10.2298/FIL1503525K.
  24. Kırık, B., Özen Zengin, F., Generalized quasi-Einstein manifolds admitting special vector fields, Acta Math. Acad. Paedagog. Nyregyhziensis, 31(1) (2015), 61–69.
  25. Prakasha, D. G., Veeresha, P., Para-Sasakian manifolds and $\ast$-Ricci solitons, Afrika Mat, 30(7-8) (2019), 989–998. https://doi.org/10.1007/s13370-019-00698-9.
  26. Shaikh, A. A., Jana, S. K. On pseudo generalized quasi-Einstein manifolds, Tamkang J. Math, 39(1) (2008), 9-24. https://doi.org/10.5556/j.tkjm.39.2008.41.
  27. Siddiqi, M. D., Akyol, M. A., $\eta$-Ricci-Yamabe solitons on Riemannian submersions from Riemannian submanifolds, arXiv:2004.14124, (2020).
  28. Sudhakar, S. K., Siddiqi, M. D., Prakasha, D. G., Invariant submanifold of hyperbolic Sasakian manifolds and $\eta$-Ricci-Bourguignon solitons, Filomat, 36(2) (2022), 409-421. https://doi.org/10.2298/FIL2202409C.
  29. Traore, M., Ndiaye, A., Sane, M., Characterizing $\phi(Ric)$-vector fields and Quasi-Einstein manifolds on multiply warped product manifolds, Int. J. Math., (2025), 5841429. https://doi.org/10.1155/ijmm/5841429.
  30. Traore, M., Ndiaye, A., Sane, M., Some results on warped product $\eta$-Ricci-Bourguignon solitons, nonlinear analysis, geometry and applications, Cham: Birkhauser, Trends Math, (2024), 299–316.
  31. Traore, M., Taştan, H. M., Blaga, A. M., Some characterizations of quasi-Einstein and twisted product manifolds, Int. J. Maps in Math, 6(1) (2023), 54-66.
  32. Traore, M., Taştan, H. M., Gerdan Aydın, S., On almost $\eta$-Ricci-Bourguignon solitons, Miskolc. Math. Notes, 25(1) (2024), 493-508. https://doi.org/10.18514/MMN.2024.4378.
  33. Traore, M., Taştan, H. M., Gerdan Aydın, S., Some characterizations on gradient almost $\eta$-Ricci-Bourguignon solitons, Bol. Soc. Paran. Mat, 43 (2025), 1-12. https://doi.org/10.5269/bspm.70710.
  34. Traore, M., Taştan, H. M., On sequential warped product $\eta$-Ricci-Bourguignon solitons, Filomat, 38(19) (2024), 6785–6797. https://doi.org/10.2298/FIL2419785T.
  35. Venkatesh, V., Naik, D. M., Aruna K. H., $\ast$-Ricci solitons and gradient almost $\ast$-Ricci solitons on Kenmotsu manifolds, Math. Slovaca, 69(6) (2019), 1447-1458. https://doi.org/10.1515/ms-2017-0321.