Almost Pseudo Symmetric Kähler Manifolds Admitting Conformal Ricci-Yamabe Metric

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-21-2023-103
Published: Sep 25, 2023
Cite as:
Sunil Kumar Yadav, Abdul Haseeb, Nargis Jamal, Almost Pseudo Symmetric Kähler Manifolds Admitting Conformal Ricci-Yamabe Metric, Int. J. Anal. Appl., 21 (2023), 103.

Main Article Content

Sunil Kumar Yadav, Abdul Haseeb, Nargis Jamal

Abstract

The novelty of the paper is to investigate the nature of conformal Ricci-Yamabe soliton on almost pseudo symmetric, almost pseudo Bochner symmetric, almost pseudo Ricci symmetric and almost pseudo Bochner Ricci symmetric Kähler manifolds. Also, we explore the harmonic aspects of conformal η-Ricci-Yamabe soliton on Kähler spcetime manifolds with a harmonic potential function f and deduce the necessary and sufficient conditions for the 1-form η, which is the g-dual of the vector field ξ on such spacetime to be a solution of Schrödinger-Ricci equation.

Article Details

References

  1. A. Gray, Einstein-Like Manifolds Which Are Not Einstein, Geom. Dedicata. 7 (1978), 259-280. https://doi.org/10.1007/bf00151525.
  2. D.E. Blair, Contact Manifolds in Riemannian Geometry, Springer Berlin Heidelberg, Berlin, Heidelberg, 1976. https://doi.org/10.1007/BFb0079307.
  3. D. Narain, S. Yadav, On Weak Concircular Symmetries of Lorentzian Concircular Structure Manifolds, Cubo. 15 (2013), 33–42. https://doi.org/10.4067/s0719-06462013000200003.
  4. N. Basu, A. Bhattacharyya, Conformal Ricci Soliton in Kenmotsu Manifold, Glob. J. Adv. Res. Class. Modern Geom. 4 (2015), 15-21.
  5. M.C. Chaki, On Pseudo Symmetric Manifolds, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 33 (1987), 53-58.
  6. G. Catino, L. Mazzieri, Gradient Einstein Solitons, Nonlinear Anal. 132 (2016), 66–94. https://doi.org/10.1016/j.na.2015.10.021.
  7. M.C. Chaki, B. Gupta, On Conformally Symmetric Spaces, Indian J. Math. 5 (1963), 113-295.
  8. B. Chow, S.C. Chu, D. Glickenstein, et al. The Ricci Flow: Techniques and Applications, American Mathematical Society, Providence, Rhode Island, 2007. https://doi.org/10.1090/surv/144.
  9. E. Cartan, Sur une Classe Remarquable d’Espaces de Riemann, Bul. Soc. Math. France. 2 (1926), 214–264. https://doi.org/10.24033/bsmf.1105.
  10. R. Deszcz, On Pseudo Symmetric Spaces, Bull. Soc. Math. Belg., Ser. A. 44 (1992), 1–34.
  11. U.C. De, S. Mallick, On Almost Pseudo Concircularly Symmetric Manifolds, J. Math. Computer Sci. 04 (2012), 317–330. https://doi.org/10.22436/jmcs.04.03.05.
  12. 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.
  13. F.Ö. Zengin, S. Altay, On Weakly and Pseudo Symmetric Riemannian Spaces, Indian J. Pure Appl. Math. 33 (2001), 1477–1488.
  14. 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.
  15. 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.
  16. 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.
  17. R.S. Hamilton, Three-Manifolds With Positive Ricci Curvature, J. Differ. Geom. 17 (1982), 255–306. https://doi.org/10.4310/jdg/1214436922.
  18. R.S. Hamilton, The Ricci Flow on Surfaces, Contemp. Math. 71 (1988), 237–261. https://cir.nii.ac.jp/crid/1571980075402918784.
  19. M. Ahmad, Gazala, M.A. Al-Shabrawi, A Note on LP-Kenmotsu Manifolds Admitting Conformal Ricci-Yamabe Solitons, Int. J. Anal. Appl. 21 (2023), 32. https://doi.org/10.28924/2291-8639-21-2023-32.
  20. 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.
  21. A. Haseeb, M. Bilal, S.K. Chaubey, et al. ζ-Conformally Flat LP-Kenmotsu Manifolds and Ricci-Yamabe Solitons, Mathematics. 11 (2022), 212. https://doi.org/10.3390/math11010212.
  22. A. Haseeb, U.C. De, η-Ricci Solitons in -Kenmotsu Manifolds, J. Geom. 110 (2019), 34. https://doi.org/10.1007/s00022-019-0490-2.
  23. A.A. Shaikh, S.K. Hui, C.S. Bagewadi, On Quasi-Conformally Flat Almost Pseudo Ricci Symmetric Manifolds, Tamsui Oxford J. Math. Sci. 26 (2010), 203–219.
  24. Z.I. Szabó, Structure Theorems on Riemannian Spaces Satisfying R(X, Y ) · R = 0. I. The Local Version, J. Differ. Geom. 17 (1982), 531–582. https://doi.org/10.4310/jdg/1214437486.
  25. L. Tamassy, T.Q. Binh, On Weakly Symmetric and Weakly Projective Symmetric Riemannian Manifolds, Coll. Math. Soc., J. Bolyai. 50 (1989), 663–670. https://cir.nii.ac.jp/crid/1571980075775193856.
  26. L. Tamassy, U.C. De, T.Q. Binh, On Weak Symmetries of Ka¨hler Manifolds, Balkan J. Geom. Appl. 5 (2000), 149–155.
  27. P. Zhang, Y. Li, S. Roy, et al. A. Bhattacharyya, Geometrical Structure in a Perfect Fluid Spacetime with Conformal Ricci-Yamabe Soliton, Symmetry. 14 (2022), 594. https://doi.org/10.3390/sym14030594.
  28. Y. Li, A. Haseeb, M. Ali, LP-Kenmotsu Manifolds Admitting η-Ricci-Yamabe Solitons and Spacetime, J. Math. 2022 (2022), 6605127. https://doi.org/10.1155/2022/6605127.