DOI QR코드

DOI QR Code

RICCI ρ-SOLITON IN A PERFECT FLUID SPACETIME WITH A GRADIENT VECTOR FIELD

  • Dibakar Dey (Department of Pure Mathematics University of Calcutta) ;
  • Pradip Majhi (Department of Pure Mathematics University of Calcutta)
  • 투고 : 2022.02.18
  • 심사 : 2022.05.16
  • 발행 : 2023.01.31

초록

In this paper, we studied several geometrical aspects of a perfect fluid spacetime admitting a Ricci ρ-soliton and an η-Ricci ρ-soliton. Beside this, we consider the velocity vector of the perfect fluid space time as a gradient vector and obtain some Poisson equations satisfied by the potential function of the gradient solitons.

키워드

과제정보

The authors would like to thank the anonymous referee for his/her careful reading and valuable suggestions that have improved the paper.

참고문헌

  1. Z. Ahsan and M. Ali, Curvature tensor for the spacetime of general relativity, Int. J. Geom. Methods Mod. Phys. 14 (2017), no. 5, 1750078, 13 pp. https://doi.org/10.1142/S0219887817500785 
  2. M. Ali and Z. Ahsan, Ricci solitons and symmetries of spacetime manifold of general relativity, J. Adv. Res. Classical Mod. Geom. 1 (2014), no. 2, 75-84. 
  3. A. M. Blaga, Solitons and geometrical structures in a perfect fluid spacetime, Rocky Mountain J. Math. 50 (2020), no. 1, 41-53. https://doi.org/10.1216/rmj.2020.50.41 
  4. A. M. Blaga, On harmonicity and Miao-Tam critical metrics in a perfect fluid spacetime, Bol. Soc. Mat. Mex. (3) 26 (2020), no. 3, 1289-1299. https://doi.org/10.1007/s40590-020-00281-4 
  5. G. Catino, L. Cremaschi, Z. Djadli, C. Mantegazza, and L. Mazzieri, The Ricci-Bourguignon flow, Pacific J. Math. 287 (2017), no. 2, 337-370. https://doi.org/10.2140/pjm.2017.287.337 
  6. M. C. Chaki and R. K. Maity, On quasi Einstein manifolds, Publ. Math. Debrecen 57 (2000), no. 3-4, 297-306.  https://doi.org/10.5486/PMD.2000.2169
  7. U. C. De and G. C. Ghosh, On quasi Einstein manifolds, Period. Math. Hungar. 48 (2004), no. 1-2, 223-231. https://doi.org/10.1023/B:MAHU.0000038977.94711.ab 
  8. U. C. De and P. Majhi, On pseudo semi-projective symmetric manifolds, J. Korean Math. Soc. 55 (2018), no. 2, 391-413. https://doi.org/10.4134/JKMS.j170252 
  9. U. C. De and L. Velimirovi'c, Spacetimes with semisymmetric energy-momentum tensor, Internat. J. Theoret. Phys. 54 (2015), no. 6, 1779-1783. https://doi.org/10.1007/s10773-014-2381-5 
  10. B. O'Neill, Semi-Riemannian Geometry, Pure and Applied Mathematics, 103, Academic Press, Inc., New York, 1983. 
  11. M. D. Siddiqi, Ricci ρ-soliton and geometrical structure in a dust fluid and viscous fluid spacetime, Bulg. J. Phys. 46 (2019), 163-173. 
  12. M. D. Siddiqi and S. A. Siddiqui, Conformal Ricci soliton and geometrical structure in a perfect fluid spacetime, Int. J. Geom. Methods Mod. Phys. 17 (2020), no. 6, 2050083, 18 pp. https://doi.org/10.1142/S0219887820500838 
  13. A. N. Siddiqui and M. D. Siddiqi, Almost Ricci-Bourguignon solitons and geometrical structure in a relativistic perfect fluid spacetime, Balkan J. Geom. Appl. 26 (2021), no. 2, 126-138.  https://doi.org/10.3390/axioms12020138
  14. L. Tam'assy and T. Q. Binh, On weakly symmetric and weakly projective symmetric Riemannian manifolds, in Differential geometry and its applications (Eger, 1989), 663-670, Colloq. Math. Soc. J'anos Bolyai, 56, North-Holland, Amsterdam, 1992. 
  15. Venkatesha and H. A. Kumara, Ricci soliton and geometrical structure in a perfect fluid spacetime with torse-forming vector field, Afr. Mat. 30 (2019), no. 5-6, 725-736. https://doi.org/10.1007/s13370-019-00679-y