A Note on LP-Kenmotsu Manifolds Admitting Conformal Ricci-Yamabe Solitons

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-21-2023-32
Published: Apr 3, 2023
Cite as:
Mobin Ahmad, Gazala, Maha Atif Al-Shabrawi, A Note on LP-Kenmotsu Manifolds Admitting Conformal Ricci-Yamabe Solitons, Int. J. Anal. Appl., 21 (2023), 32.

Main Article Content

Mobin Ahmad, Gazala, Maha Atif Al-Shabrawi

Abstract

In the current note, we study Lorentzian para-Kenmotsu (in brief, LP-Kenmotsu) manifolds admitting conformal Ricci-Yamabe solitons (CRYS) and gradient conformal Ricci-Yamabe soliton (gradient CRYS). At last by constructing a 5-dimensional non-trivial example we illustrate our result.

Article Details

References

  1. N. Basu, A. Bhattacharyya, Conformal Ricci Soliton in Kenmotsu Manifold, Glob. J. Adv. Res. Class. Mod. Geom. 4 (2015), 15-21.
  2. A. M. Blaga, Some Geometrical Aspects of Einstein, Ricci and Yamabe Solitons, J. Geom. Symmetry Phys. 52 (2019), 17-26. https://doi.org/10.7546/jgsp-52-2019-17-26.
  3. S. Chidananda, V. Venkatesha, Yamabe and Riemann Solitons on Lorentzian Para-Sasakian Manifolds, Commun. Korean Math. Soc. 37 (2022), 213-228. https://doi.org/10.4134/CKMS.C200365.
  4. 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.
  5. A.E. Fischer, An Introduction to Conformal Ricci Flow, Class. Quantum Grav. 21 (2004), S171-S218. https://doi.org/10.1088/0264-9381/21/3/011.
  6. D. Ganguly, S. Dey, A. Ali, A. Bhattacharyya, Conformal Ricci Soliton and Quasi-Yamabe Soliton on Generalized Sasakian Space Form, J. Geom. Phys. 169 (2021), 104339. https://doi.org/10.1016/j.geomphys.2021.104339.
  7. 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.
  8. R.S. Hamilton, The Ricci Flow on Surfaces, Mathematics and General Relativity, Contemp. Math. 71 (1988), 237-262.
  9. A. Haseeb, M. Bilal, S.K. Chaubey, A.A.H. Ahmadini, ζ-Conformally Flat LP-Kenmotsu Manifolds and Ricci–Yamabe Solitons, Mathematics, 11 (2023), 212. https://doi.org/10.3390/math11010212.
  10. A. Haseeb, S.K. Chaubey, M.A. Khan, Riemannian 3-Manifolds and Ricci-Yamabe Solitons, Int. J. Geom. Methods Mod. Phys. 20 (2023), 2350015. https://doi.org/10.1142/s0219887823500159.
  11. A. Haseeb, R. Prasad, Certain Results on Lorentzian Para-Kenmotsu Manifolds, Bol. Soc. Parana. Mat. 39 (2021), 201–220. https://doi.org/10.5269/bspm.40607.
  12. A. Haseeb, R. Prasad, Some results on Lorentzian para-Kenmotsu manifolds, Bull. Transilvania Univ. Brasov. 13(62) (2020), 185-198. https://doi.org/10.31926/but.mif.2020.13.62.1.14.
  13. Y. Li, A. Haseeb, M. Ali, LP-Kenmotsu Manifolds Admitting η-Ricci Solitons and Spacetime, J. Math. 2022 (2022), 6605127. https://doi.org/10.1155/2022/6605127.
  14. M.A. Lone, I.F. Harry, Ricci Solitons on Lorentz-Sasakian Space Forms, J. Geom. Phys. 178 (2022), 104547. https://doi.org/10.1016/j.geomphys.2022.104547.
  15. Pankaj, S.K. Chaubey, R. Prasad, Three-Dimensional Lorentzian Para-Kenmotsu Manifolds and Yamabe Solitons, Honam Math. J. 43 (2021), 613-626. https://doi.org/10.5831/HMJ.2021.43.4.613.
  16. J.P. Singh, M. Khatri, On Ricci-Yamabe Soliton and Geometrical Structure in a Perfect Fluid Spacetime, Afr. Mat. 32 (2021), 1645–1656. https://doi.org/10.1007/s13370-021-00925-2.
  17. H.I. Yoldaş, On Kenmotsu Manifolds Admitting η-Ricci-Yamabe Solitons, Int. J. Geom. Methods Mod. Phys. 18 (2021), 2150189. https://doi.org/10.1142/s0219887821501899.
  18. K. Yano, Integral Formulas in Riemannian Geometry, Pure and Applied Mathematics, Vol. I, Marcel Dekker, New York, 1970.
  19. K. Yano, M. Kon, Structures on Manifolds, World Scientific Publishing Co., Singapore, 1984.
  20. 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.