k-Yamabe and quasi k-Yamabe solitons on imperfect fluid generalized Robertson - Walker spacetime

k-Yamabe and quasi k-Yamabe solitons on imperfect fluid generalized Robertson - Walker spacetime

Автор: Siddiqi Mohd Danish, Siddiqui Shah Alam

Журнал: Математическая физика и компьютерное моделирование @mpcm-jvolsu

Рубрика: Математика и механика

Статья в выпуске: 1 т.25, 2022 года.

Бесплатный доступ

In this research article, we estimate the behavior of an imperfect fluid generalized Robertson - Walker spacetime (𝐺𝑅𝑊) in terms of 𝑘-Yamabe soliton with torseforming vector field. Besides this, we evaluate a specific situation when the potential vector filed is of the form of gradient i.e., = grad(Ψ), we extract a Laplace - Poisson equation, and Liouville equation from the quasi 𝑘-Yamabe soliton equation.

𝑘-yamabe soliton, quasi 𝑘-yamabe soliton, imperfect fluid generalized robertson - walker spacetime, torse-forming vector field, einstein manifold

Короткий адрес: https://sciup.org/149140096

IDR: 149140096

Список литературы k-Yamabe and quasi k-Yamabe solitons on imperfect fluid generalized Robertson - Walker spacetime

  • Alias L., Romero A., Sanchez M. Uniqueness of Complete Spacelike Hypersurfaces of Constant Mean Curvature in Generalized Robertson — Walker Spacetimes. Gen. Relativ. Gravit, 1995, vol. 27, iss. 1, pp. 71-84. DOI: https://doi.org/10.1007/BF02105675.
  • Ali M., Ahsan Z. Ricci Solitons and Symmetries of Space Time Manifold of General Relativity. Journal of Advanced Research on Classical and Modern Geometries, 2014, vol. 1, iss. 2, pp. 75-84.
  • Ahsan Z., Siddiqui S.A. Concircular Curvature Tensor and Fluid Spacetimes. Int. J. Theor Phys, 2009, vol. 48, iss. 11, pp. 3202-3212. DOI: https://doi.org/10.1007/s10773-009-0121-z.
  • Blaga A.M. Harmonic Aspects in an n-Ricci Soliton. Int. Elect. J. Geom., 2020, vol. 13, iss. 1, pp. 41-49.
  • Blaga A.M. On Gradient n-Einstein Solitons. Kragujevac J. Math, 2018, vol. 42, iss. 2, pp. 229-237.
  • Blaga A.M. Solitons and Geometrical Structures in a Perfect Fluid Spacetime. Rocky Mountain J. Math, 2020, vol. 50, no. 1, pp. 41-53. DOI: https://doi.org/10.48550/arXiv.1705.04094.
  • Catino G., Mazzieri L. Gradient Einstein Solitons. Nonlinear Anal, 2016, vol. 132, pp. 66-94.
  • Chaki M.C., Ray S. Space-Times with Covariant-Constant Energy-Momentum Tensor. Int. J. Theor Phys, 1996, vol. 35, iss. 5, pp. 1027-1032. DOI: https://doi.org/10.1007/BF02302387.
  • Chaubey S.K. Generalized Robertson — Walker Space-Times with W\-Curvature Tensor. J. Phys Math., 2019, vol. 10, iss. 2, article ID: 1000303.
  • Chen B.-Y. A Simple Characterization of Generalized Robertson — Walker Spacetime. Gen. Relativity Gravit, 2014, vol. 46, article ID: 1833. DOI: https://doi.org/10.1007/s10714-014-1833-9.
  • Chen B.Y., Desahmukh S. Yamabe and Quasi-Yamabe Soliton on Euclidean Submanifolds. Mediterranean Journal of Mathematics, 2018, vol. 15, article ID: 194. DOI: https://doi.org/10.1007/s00009-018-1237-2.
  • Crasmareanu M. Last Multipliers on Weighted Manifolds and the Weighted Liouville Equation. UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, 2015, vol. 77, iss. 3, pp. 53-58.
  • Cui X., Chen X. The fc-Almost Yamabe Solitons and Contact Metric Manifolds. Rocky Mountain J. Math., 2021, vol. 51, iss. 1, pp. 125-137. DOI: https://doi.org/10.1216/rmj.2021.51.125.
  • Duggal K. Almost Ricci Solitons and Physical Applications. International Electronic Journal of Geometry V, 2017, vol. 10, iss. 2, pp. 1-10.
  • De U.C., Ghosh G.C. On Quasi Einstein Manifolds. Period. Math. Hungar, 2004, vol. 48, iss. 12, pp. 223-231. DOI: https://doi.org/10.1023/B:MAHU.0000038977.94711.ab.
  • De U.C., Velimirovic L. Spacetimes with Semisymmetric Energy-Momentum Tensor. Int. J. Theor Phys., 2015, vol. 54, pp. 1779-1783. DOI: https://doi.org/10.1007/s10773-014-2381-5.
  • Hamilton R.S. The Ricci Flow on Surfaces. Mathematics and General Relativity. Santa Cruz, Amer. Math. Soc., 1988, vol. 71, pp. 237-262.
  • Jun J.B., Siddiqi M.D. Almost Quasi-Yamabe Solitons on Lorentzian Concircular Structure Manifolds-[(LC5)raj. Honam Mathematical Journal, 2020, vol. 42, iss. 3, pp. 521536.
  • Katz M. Liouville's Equation for Curvature and Systolic Defect. arXiv:1105.0553v2[math.DG]. URL: https://arxiv.org/abs/1105.0553.
  • Kim J. A Type of Conformal Curvature Tensor. Far East J. Math. Sci., 2016, vol. 99, iss. 1, pp. 61-74. DOI: https://doi.org/10.17654/MS099010061.
  • Kim J. On Pseudo Semiconformally Symmetric Manifolds. Bull. Korean Math. Soc., 2017, vol. 54, iss. 1, pp. 177-186. DOI: https://doi.org/10.4134/BKMS.b151007.
  • Mantica C.A., Molinari L.G., De U.C. A Condition for a Perfect Fluid Spacetime to be a Generalized Robertson — Walker Spacetimes, a Survey. J. Math. Phys., 2016, vol. 57, no. 2, article ID: 049901. DOI: https://doi.org/10.1063/L4941942.
  • Mantica C.A., Suh Y.J, De U.C. A Note on Generalized Robertson — Walker Spacetimes. Int. J. Geom. Math. Mod. Phys., 2016, vol. 13, no. 6, article ID: 1650079. DOI: https://doi.org/10.1142/S0219887816500791.
  • Mantica C.A., Molinari L.G. Generalized Robertson — Walker Spacetimes — A Survey. Int. J. Geom. Math. Mod. Phys, 2017, vol. 14, no. 3, article ID: 102502. DOI: https://doi.org/10.1142/S021988781730001X.
  • Novello M., Reboucas M.J. The Stability of a Rotating Universe. Astrophys. J., 1978, vol. 225, pp. 719-724.
  • O'Neill B. Semi-Riemannian Geometry with Applications to Relativity. New York, Academic Press, 1983. xii, 468 p.
  • Sanchez M. On the Geometry of Generalized Robertson — Walker Spacetime Geodesics. Gen. Relativ. Gravit., 1998, vol. 27, pp. 71-84.
  • Shaikh A.A., Jana S.K. A Pseudo-Quasi-Conformal Curvature Tensor on a Riemannian Manifold. South East Asian J. Math. Math. Sci., 2005, vol. 4, iss. 1, pp. 15-20.
  • Siddiqi M.D., Siddiqui S.A. Conformal Ricci Soliton and Geometrical Structure in a Perfect Fluid Spacetime. Int. J. Geom. Methods Mod. Phys., 2020, vol. 17, iss. 6, article ID: 2050083. DOI: https://doi.org/10.1142/S0219887820500838.
  • Siddiqi M.D. Generalized Yamabe Solitons on Trans-Sasakian Manifolds. Bulletin of Institute of Mathematics, 2020, iss. 3, pp. 77-85.
  • Siddiqi M.D. Ricci p-Soliton and Geometrical Structure in a Dust Fluid and Viscous Fluid Spacetime. Bulg. J. Phys., 2019, vol. 46, pp. 163-173.
  • Stephani H. General Relativity-An Introduction to the Theory of Gravitational Field. Cambridge, Cambridge University Press, 1982. 314 p.
  • Venkatesha V., Kumara H.A. Ricci Solitons and Geometrical Structure in a Perfect Fluid Spacetime with Torse-Forming Vector Filed. Afrika Mathematika, 2019, vol. 30, pp. 725-736. DOI: https://doi.org/10.1007/s13370-019-00679-y.
  • Yano K. Integral Formulas in Riemannian Geometry. New York, Marcel Dekker, 1970. 466 p. DOI: https://doi.org/10.1017/S0008439500031520.
  • Yano K. On Torse Forming Direction in a Riemannian Space. Proc. Imp. Acad. Tokyo, 1994, vol. 20, pp. 340-345.
  • Yau S.T. Harmonic Functions on Complete Riemannian Manifolds. Commu. Pure. Appl. Math, 1975, vol. 28, pp. 201-228.
Еще
Статья научная
SciUp 2024 © 2024 ©