η̈-Ricci Soliton and Its Applications on φ-Recurrent LP Sasakian Manifold

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-22-2024-200
Published: Oct 31, 2024
Cite as:
Pankaj Pandey, Kamakshi Sharma, B.B. Chaturvedi, Mohammad Nazrul Islam Khan, η̈-Ricci Soliton and Its Applications on φ-Recurrent LP Sasakian Manifold, Int. J. Anal. Appl., 22 (2024), 200.

Main Article Content

Pankaj Pandey, Kamakshi Sharma, B.B. Chaturvedi, Mohammad Nazrul Islam Khan

Abstract

The objective of this paper is to study the φ-recurrent nature and application of LP-Sasakian manifold associated with η̈ -Ricci soliton. Initially, we introduce an example to show the existance of LP Sasakian manifold equipped with η̈ -Ricci soliton. The idea of Ricci soliton recognized as a generalization of an Einstein metric and governing as the solution of partial differential equations representing Ricci flow. Some conditions have been obtained representing the nature of soliton (expanding, unchanged and shrinkingness) in pseudo projective, Weyl projective and semi generlized curvature with φ-recurrent condition. The application of η̈ -Ricci Soliton on spacetime also discussed.

Article Details

References

  1. P. Almia, J. Upreti, Certain Properties of η-Ricci Soliton on η-Einstein Para-Kenmotsu Manifolds, Filomat 37 (2023), 9575–9585. https://doi.org/10.2298/FIL2328575A.
  2. M.B. Ayed, K.E. Mehdi, Multiplicity Results for the Scalar Curvature Problem on Half Spheres, Discr. Contin. Dyn. Syst. 44 (2024), 1878–1900. https://doi.org/10.3934/dcds.2024013.
  3. S. Elsaeed, O. Moaaz, K.S. Nisar, M. Zakarya, E.M. Elabbasy, Sufficient Criteria for Oscillation of Even-Order Neutral Differential Equations with Distributed Deviating Arguments, AIMS Math. 9 (2024), 15996–16014. https://doi.org/10.3934/math.2024775.
  4. B.B. Chaturvedi, P. Bhagat, M.N.I. Khan, Novel Theorems for a Bochner Flat Lorentzian Kahler Space-Time Manifold with η-Ricci-Yamabe Solitons, Chaos Solitons Fractals: X 11 (2023), 100097. https://doi.org/10.1016/j.csfx.2023.100097.
  5. S.K. Chaubey, U.C. De, Three-Dimensional Riemannian Manifolds and Ricci Solitons, Quaest. Math. 45 (2022), 765–778. https://doi.org/10.2989/16073606.2021.1895352.
  6. 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.
  7. N. Omar, S. Serra-Capizzano, B. Qaraad, F. Alharbi, O. Moaaz, E.M. Elabbasy, More Effective Criteria for Testing the Oscillation of Solutions of Third-Order Differential Equations, Axioms 13 (2024), 139. https://doi.org/10.3390/axioms13030139.
  8. S. Dey, Conformal Ricci Soliton and Almost Conformal Ricci Soliton in Paracontact Geometry, Int. J. Geom. Methods Modern Phys. 20 (2023), 2350041. https://doi.org/10.1142/S021988782350041X.
  9. K. De, M.N.I. Khan, U.C. De, Characterizations of Generalized Robertson-Walker Spacetimes Concerning Gradient Solitons, Heliyon 10 (2024), e25702. https://doi.org/10.1016/j.heliyon.2024.e25702.
  10. U.C. De, M.N.I. Khan, A. Sardar, h-Almost Ricci-Yamabe Solitons in Paracontact Geometry, Mathematics 10 (2022), 3388. https://doi.org/10.3390/math10183388.
  11. U.C. De, A. Sardar, K. De, Ricci-Yamabe Solitons and 3-Dimensional Riemannian Manifolds, Turk. J. Math. 46 (2022), 1078–1088. https://doi.org/10.55730/1300-0098.3143.
  12. U.C. De, A.A. Shaikh, S. Biswas, On φ–Recurrent Sasakian Manifolds, Novi Sad J. Math. 33 (2003), 43–48.
  13. R.S. Hamilton, Three-Manifolds with Positive Ricci Curvature, J. Diff. Geom. 17 (1982), 255–306.
  14. A. Haseeb, M. Bilal, S.K. Chaubey, M.N.I. Khan, Geometry of Indefinite Kenmotsu Manifolds as ∗η-Ricci-Yamabe Solitons, Axioms 11 (2022), 461. https://doi.org/10.3390/axioms11090461.
  15. A. Haseeb, S.K. Chaubey, Lorentzian Para-Sasakian Manifolds and *-Ricci Solitons, Kragujevac J. Math. 48 (2024), 167–179.
  16. S.K. Hui, R.S. Lemence, D. Chakraborty, Ricci Solitons on Ricci Pseudosymmetric (LCS)n-Manifolds, arXiv:1707.03618 [math.DG], (2017). http://arxiv.org/abs/1707.03618.
  17. S. Hui, S. Yadav, A. Patra, Almost Conformal Ricci Solitons on f-Kenmotsu Manifolds, Khayyam J. Math. 5 (2019), 89–104. https://doi.org/10.22034/kjm.2019.81221.
  18. P. Majhi, D. Kar, Eta-Ricci Solitons on LP-Sasakian Manifolds, Rev. Union Mat. Argentina 60 (2019), 391–405. https://doi.org/10.33044/revuma.v60n2a07.
  19. Y. ChandraMandal, S. Kumar Hui, Yamabe Solitons with Potential Vector Field as Torse Forming, Cubo (Temuco) 20 (2018), 37–47. https://doi.org/10.4067/S0719-06462018000300037.
  20. K. Matsumoto, On Lorentzian Paracontact Manifolds, Bull. Yamagata Univ. Nat. Sci. 12 (1989), 151–156.
  21. T. Mert, M. Atçeken, On the Almost η-Ricci Solitons on Pseudosymmetric Lorentz Generalized Sasakian Space Forms, Univ. J. Math. Appl. 6 (2023), 43–52. https://doi.org/10.32323/ujma.1236596.
  22. H.G. Nagaraja, K. Venu, Ricci Solitons in Kenmotsu Manifold, J. Inf. Math. Sci. 8 (2016), 29–36.
  23. P. Pandey, On Weakly Cyclic Generalized Z-Symmetric Manifolds, Nat. Acad. Sci. Lett. 43 (2020), 347–350. https://doi.org/10.1007/s40009-020-00875-6.
  24. P. Pandey, B.B. Chaturvedi, On a Lorentzian Complex Space Form, Nat. Acad. Sci. Lett. 43 (2020), 351–353. https://doi.org/10.1007/s40009-020-00874-7.
  25. P. Pandey, K. Sharma, Some Results on Ricci Soliton on Contact Metric Manifolds, Facta Univ. Ser: Math. Inf. 38 (2023), 473–486.
  26. P. Pandey, K. Sharma, Generalized Z-Ricci Soliton on Sasakian 3-Manifold with Generalized Z-Tensor, AIP Conf. Proc. 3087 (2024), 060001. https://doi.org/10.1063/5.0199390.
  27. R. Poddar, S. Balasubramanian, R. Sharma, Yamabe Solitons in Contact Geometry, N. Z. J. Math. 54 (2023), 49–55. https://doi.org/10.53733/286.
  28. A. Sardar, M.N.I. Khan, U.C. De, η-∗-Ricci Solitons and Almost Co-Kähler Manifolds, Mathematics 9 (2021), 3200. https://doi.org/10.3390/math9243200.
  29. A. Sardar, U.C. De, A. Gezer, η-∗-Ricci Solitons and Paracontact Geometry, J. Anal. 31 (2023), 2861–2876. https://doi.org/10.1007/s41478-023-00620-4.
  30. S. Sarkar, S. Dey, ∗-Conformal η-Ricci Soliton within the Framework of Kenmotsu Manifolds, Ricerche Mat. (2023). https://doi.org/10.1007/s11587-023-00781-1.
  31. M.D. Siddiqi, O. Bahadır, Eta-Ricci Solitons on Kenmotsu Manifold With Generalized Symmetric Metric Connection, Facta Univ. Ser.: Math. Inf. 35 (2020), 295–310. https://doi.org/10.22190/FUMI2002295S.
  32. A.A. Shaikh, D.G. Prakasha, H. Ahmad, On Generalized φ-Recurrent LP-Sasakian Manifolds, J. Egypt. Math. Soc. 23 (2015), 161–166. https://doi.org/10.1016/j.joems.2013.12.019.
  33. A.A. Shaikh, S. Biswas, On LP-Sasakian Manifolds, Bull. Malays. Math. Sci. Soc. 27 (2004), 17–26.
  34. B. Shanmukha, V. Venkatesha, Some Ricci Solitons on Kenmotsu Manifold, J. Anal. 28 (2020), 1155–1164. https://doi.org/10.1007/s41478-020-00243-z.
  35. G.S. Shivaprasanna, M.S. Haque, G. Somashekhara, η-Ricci Soliton on f-Kenmotsu Manifolds, J. Phys.: Conf. Ser. 1543 (2020), 012007. https://doi.org/10.1088/1742-6596/1543/1/012007.
  36. M.D. Siddiqi, S.K. Chaubey, M.N.I. Khan, f(R, T)-Gravity Model with Perfect Fluid Admitting Einstein Solitons, Mathematics 10 (2021), 82. https://doi.org/10.3390/math10010082.
  37. A. Singh, R.K. Pandey, A. Prakash, K. Sachin, On a Pseudo Projective φ-Recurrent Sasakian Manifolds, J. Math. Computer Sci. 14 (2015), 309–314.
  38. Venkatesha, C.S. Bagewadi, K.T. Pradeep Kumar, Some Results on Lorentzian Para-Sasakian Manifolds, ISRN Geom. 2011 (2011), 161523. https://doi.org/10.5402/2011/161523.
  39. S.V. Vishnuvardhana, Venkatesha, S.K. Hui, Certain Results on (LCS)n-Manifolds, arXiv:1901.06873 [math.DG], (2019). https://doi.org/10.48550/ARXIV.1901.06873.