Almost ∗-Ricci Soliton on α-paraSasakian Manifold

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-22-2024-180
Published: Oct 3, 2024
Cite as:
Kanika Sood, Khushbu Srivastava, Sachin Kumar Srivastava, Mohammad Nazrul Islam Khan, Almost ∗-Ricci Soliton on α-paraSasakian Manifold, Int. J. Anal. Appl., 22 (2024), 180.

Main Article Content

Kanika Sood, Khushbu Srivastava, Sachin Kumar Srivastava, Mohammad Nazrul Islam Khan

Abstract

It has been noted that if the ∗-Ricci tensor used to define ∗-Ricci soliton is a constant multiple of the metric tensor g(ei,ej), for all ei, ej orthogonal to characteristic vector field ξ, then the manifold is ∗-Einstein manifold. The metric associated with ∗-Einstein manifold is ∗-Einstein metric, and the ∗-Ricci soliton is its generalization. In this paper we study an almost ∗-Ricci soliton (g, W, λ) and an almost gradient ∗-Ricci soliton (g, grad (ρ), λ) by means of mathematical operators on (2m+1)-dimensional α-paraSasakian manifold S2m+1.

Article Details

References

  1. R.S. Hamilton, The Ricci flow on surfaces, Mathematics and General Relativity, Contemp. Math. 71 (1988), 237–261. https://cir.nii.ac.jp/crid/1573105975542168832.
  2. G. Kaimakamis, K. Panagiotidou, ∗-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.
  3. S. Tachibana, On Almost-Analytic Vectors in Almost-Kählerian Manifolds, Tohoku Math. J. 11 (1959), 247–265. https://doi.org/10.2748/tmj/1178244584.
  4. T. Hamada, Real Hypersurfaces of Complex Space Forms in Terms of Ricci ∗-Tensor, Tokyo J. Math. 25 (2002), 473–483. https://doi.org/10.3836/tjm/1244208866.
  5. K. De, A Note on Gradient ∗-Ricci Solitons, Math. Sci. Appl. E-Notes 8 (2020), 79–85. https://doi.org/10.36753/mathenot.727083.
  6. X. Chen, Real Hypersurfaces With ∗-Ricci Tensors in Complex Two-Plane Grassmannians, Bull. Korean Math. Soc. 54 (2017), 975–992. https://doi.org/10.4134/BKMS.B160414.
  7. R.S. Gupta, S. Rani, ∗-Ricci Soliton on GSSF with Sasakian Metric, Note Mat. 42 (2022), 95–108. https://doi.org/10.1285/i15900932v42n1p95.
  8. R. Ma, D. Pei, ∗-Ricci Tensor on (κ, µ)-Contact Manifolds, AIMS Math. 7 (2022), 11519–11528. https://doi.org/10.3934/math.2022642.
  9. M. Ben Ayed, K. El 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. K. De M.N.I. Khan, U.C. De, Almost co-Kähler Manifolds and (m, ρ)-Quasi-Einstein Solitons, Chaos Solitons Fractals, 167 (2023), 113050. https://doi.org/10.1016/j.chaos.2022.113050.
  15. A. Haseeb, S.K. Chaubey, F. Mofarreh, A.A.H. Ahmadini, A Solitonic Study of Riemannian Manifolds Equipped with a Semi-Symmetric Metric ξ-Connection, Axioms 12 (2023), 809. https://doi.org/10.3390/axioms12090809.
  16. D.G. Prakasha, M.R. Amruthalakshmi, F. Mofarreh, A. Haseeb, Generalized Lorentzian Sasakian-Space-Forms with M-Projective Curvature Tensor, Mathematics 10 (2022), 2869. https://doi.org/10.3390/math10162869.
  17. S. Kumar, M. Bilal, R. Prasad, A. Haseeb, Z. Chen, V-Quasi-Bi-Slant Riemannian Maps, Symmetry 14 (2022), 1360. https://doi.org/10.3390/sym14071360.
  18. A. Haseeb, M. Bilal, S.K. Chaubey, A.A.H. Ahmadini, ξ-Conformally Flat LP-Kenmotsu Manifolds and RicciYamabe Solitons, Mathematics 11 (2022), 212. https://doi.org/10.3390/math11010212.
  19. U.C. De, Y.J. Suh, S.K. Chaubey, Semi-Symmetric Curvature Properties of Robertson–Walker Spacetimes, Z. Mat. Fiz. Anal. Geom. 18 (2022), 368–381. https://doi.org/10.15407/mag18.03.368.
  20. 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.
  21. G. Calvaruso, A. Perrone, Ricci Solitons in Three-Dimensional Paracontact Geometry, J. Geom. Phys. 98 (2015), 1–12. https://doi.org/10.1016/j.geomphys.2015.07.021.
  22. U.C. De, K. Mandal, Ricci Almost Solitons and Gradient Ricci Almost Solitons in (k, µ)-Paracontact Geometry, Bol. Soc. Paran. Mat. 37 (2017), 119–130. https://doi.org/10.5269/bspm.v37i3.33027.
  23. D.S. Patra, Ricci Solitons and Paracontact Geometry, Mediterr. J. Math. 16 (2019), 137. https://doi.org/10.1007/s00009-019-1419-6.
  24. 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.
  25. R. Sharma, A. Ghosh, Sasakian 3-Manifold as a Ricci Soliton Represents the Heisenberg Group, Int. J. Geom. Methods Mod. Phys. 08 (2011), 149–154. https://doi.org/10.1142/s021988781100504x.
  26. M.N.I. Khan, S.K. Chaubey, N. Fatima, A. Al Eid, Metallic Structures for Tangent Bundles over Almost Quadratic φ-Manifolds, Mathematics 11 (2023), 4683. https://doi.org/10.3390/math11224683.
  27. M.N.I. Khan, U.C. De, L.S. Velimirovic, Lifts of a Quarter-Symmetric Metric Connection from a Sasakian Manifold to Its Tangent Bundle, Mathematics 11 (2022), 53. https://doi.org/10.3390/math11010053.
  28. S. Kaneyuki, F.L. Williams, Almost Paracontact and Parahodge Structures on Manifolds, Nagoya Math. J. 99 (1985), 173–187. https://doi.org/10.1017/s0027763000021565.
  29. A. Ghosh, D.S. Patra, ∗-Ricci Soliton Within the Frame-Work of Sasakian and (k, µ)-Contact Manifold, Int. J. Geom. Methods Mod. Phys. 15 (2018), 1850120. https://doi.org/10.1142/s0219887818501207.
  30. S. Zamkovoy, G. Nakova, The Decomposition of Almost Paracontact Metric Manifolds in Eleven Classes Revisited, J. Geom. 109 (2018), 18. https://doi.org/10.1007/s00022-018-0423-5.
  31. K. Matsumoto, Conformal Killing Vector Fields in a P-Sasakian Manifold, J. Korean Math. Soc. 14 (1977), 135–142.
  32. K. Yano, Integral Formulas in Riemannian Geometry, Marcel Dekker, New York, 1970.