Geometry of Certain Almost Conformal Metrics in f(R)-Gravity

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DOI: https://doi.org/10.28924/2291-8639-23-2025-76
Published: Mar 24, 2025
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Rajendra Prasad, Abhinav Verma, Mohd Bilal, Abdul Haseeb, Vindhyachal Singh Yadav, Geometry of Certain Almost Conformal Metrics in f(R)-Gravity, Int. J. Anal. Appl., 23 (2025), 76.

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Rajendra Prasad, Abhinav Verma, Mohd Bilal, Abdul Haseeb, Vindhyachal Singh Yadav

Abstract

In this article, we explore certain almost conformal Ricci solitons in f(R)-gravity by assuming the potential vector field as a concircular vector field. We also study the almost conformal gradient-Ricci solitons and the almost conformal ω-Ricci solitons in f(R)-gravity. Furthermore, it is shown that an almost conformal ω-Ricci soliton and an almost conformal ω-Ricci-Yamabe soliton establish Poisson’s equation. At the last, some examples are constructed.

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References

  1. R.S. Hamilton, Lectures on Geometric Flows, Lecture Notes, (1989).
  2. R.S. Hamilton, The Ricci Flow on Surfaces, in: J.A. Isenberg (Ed.), Contemporary Mathematics, American Mathematical Society, Providence, Rhode Island, 1988: pp. 237–262. https://doi.org/10.1090/conm/071/954419.
  3. B.B. Sinha, R. Sharma, On Para-A-Einstein Manifolds, Publ. Inst. Math. (Beogr.), Nouv. Sér. 34 (1983), 211-215. https://eudml.org/doc/258502.
  4. C.L. Bejan, M. Crasmareanu, Ricci Solitons in Manifolds with Quasi-Constant Curvature, Publ. Math. Debrecen 78 (2011), 235–243. https://doi.org/10.5486/PMD.2011.4797.
  5. C. Calin, M. Crasmareanu, From the Eisenhart Problem to Ricci Solitons in ˇ f-Kenmotsu Manifolds, Bull. Malays. Math. Sci. Soc. 33 (2010), 361-368. http://eudml.org/doc/244370.
  6. B.Y. CHEN, Some Results on Concircular Vector Fields and Their Applications to Ricci Solitons, Bull. Korean Math. Soc. 52 (2015), 1535–1547. https://doi.org/10.4134/BKMS.2015.52.5.1535.
  7. J.T. Cho, M. Kimura, Ricci Solitons and Real Hypersurfaces in a Complex Space Form, Tohoku Math. J. 61 (2009), 205-212. https://doi.org/10.2748/tmj/1245849443.
  8. A. Haseeb, R. Prasad, η-Ricci Solitons on ∈-LP-Sasakian Manifolds With a Quarter-Symmetric Metric Connection, Honam Math. J. 41 (2019), 539–558. https://doi.org/10.5831/HMJ.2019.41.3.539.
  9. R. Prasad, A. Verma, V.S. Yadav, Characterization of Perfect Fluid Lorentzian α-Para Kenmotsu Spacetimes, Ganita 73 (2023), 89-104.
  10. S.K. Hui, R. Prasad, T. Pal, Ricci Solitons on Submanifolds of (LCS)n-Manifolds, Ganita 68 (2018), 53-63.
  11. S. Pigola, M. Rigoli, M. Rimoldi, A.G. Setti, Ricci Almost Solitons, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 10 (2011), 757-799.
  12. A.E. Fischer, An Introduction to Conformal Ricci Flow, Class. Quantum Gravity 21 (2004), S171-S218. https://doi.org/10.1088/0264-9381/21/3/011.
  13. N. Basu, A. Bhattacharya, Conformal Ricci Soliton in Kenmotsu Manifold, Glob. J. Adv. Res. Class. Mod. Geom. 4 (2015), 15-21.
  14. S. Güler, M. Crasmareanu, Ricci–Yamabe Maps for Riemannian Flows and Their Volume Variation and Volume Entropy, Turk. J. Math. 43 (2019), 2631–2641. https://doi.org/10.3906/mat-1902-38.
  15. G. Catino, L. Cremaschi, Z. Djadli, C. Mantegazza, L. Mazzieri, The Ricci–Bourguignon Flow, Pac. J. Math. 287 (2017), 337–370. https://doi.org/10.2140/pjm.2017.287.337.
  16. G. Catino, L. Mazzieri, Gradient Einstein Solitons, Nonlinear Anal. 132 (2016), 66–94. https://doi.org/10.1016/j.na.2015.10.021.
  17. H.A. Buchdahl, Non-Linear Lagrangians and Cosmological Theory, Mon. Not. R. Astron. Soc. 150 (1970), 1–8. https://doi.org/10.1093/mnras/150.1.1.
  18. K. De, U.C. De, Investigations on Solitons in f(R)-Gravity, Eur. Phys. J. Plus 137 (2022), 180. https://doi.org/10.1140/epjp/s13360-022-02399-y.
  19. K. De, U.C. De, Ricci-Yamabe Solitons in f(R)-Gravity, Int. Electron. J. Geom. 16 (2023), 334–342. https://doi.org/10.36890/iejg.1234057.
  20. P.H. Chavanis, Cosmology with a Stiff Matter Era, Phys. Rev. D. 92 (2015), 103004. https://doi.org/10.1103/PhysRevD.92.103004.
  21. A. Fialkow, Conformal Geodesics, Trans. Amer. Math. Soc. 45 (1939), 443–473. https://doi.org/10.1090/S0002-9947-1939-1501998-9.
  22. B. O’Neill, Semi-Riemannian Geometry: With Applications to Relativity, Academic Press, New York, 1983.
  23. S. Sarkar, S. Dey, A.H. Alkhaldi, A. Bhattacharyya, Geometry of Para-Sasakian Metric as an Almost Conformal η-Ricci Soliton, J. Geom. Phys. 181 (2022), 104651. https://doi.org/10.1016/j.geomphys.2022.104651.
  24. Y. Li, S. Dey, S. Pahan, A. Ali, Geometry of Conformal η-Ricci Solitons and Conformal η-Ricci Almost Solitons on Paracontact Geometry, Open Math. 20 (2022), 574–589. https://doi.org/10.1515/math-2022-0048.
  25. R. Prasad, V. Kumar, Conformal η-Ricci Soliton in Lorentzian Para Kenmotsu Manifolds, Gulf J. Math. 14 (2023), 54–67. https://doi.org/10.56947/gjom.v14i2.931.
  26. T. Dutta, N. Basu, A. Bhattacharyya, Almost Conformal Ricci Solituons on 3-Dimensional Trans-Sasakian Manifold, Hacettepe J. Math. Stat. 45 (2016), 1379-1392.
  27. A. Haseeb, M.A. Khan, Conformal η-Ricci-Yamabe Solitons within the Framework of -LP-Sasakian 3-Manifolds, Adv. Math. Phys. 2022 (2022), 3847889. https://doi.org/10.1155/2022/3847889.
  28. R. Prasad, A. Haseeb, V. Kumar, η-Ricci-Yamabe and ∗-η-Ricci-Yamabe Solitons in Lorentzian Para-Kenmotsu Manifolds, Analysis 44 (2024), 375–384. https://doi.org/10.1515/anly-2023-0039.
  29. P. Zhang, Y. Li, S. Roy, S. Dey, A. Bhattacharyya, Geometrical Structure in a Perfect Fluid Spacetime with Conformal Ricci–Yamabe Soliton, Symmetry 14 (2022), 594. https://doi.org/10.3390/sym14030594.
  30. S.K. Chaubey, A. Haseeb, Conformal η-Ricci-Yamabe Solitons in the Framework of Riemannian Manifolds, in: B.Y. Chen, M.A. Choudhary, M.N.I. Khan (Eds.), Geometry of Submanifolds and Applications, Springer, Singapore, 2024: pp. 209–224. https://doi.org/10.1007/978-981-99-9750-3_13.