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* Ricci Solitons and Symmetries of Type D Gravitational Fields in Spacetime Manifolds

Year 2021, Volume: 2 Issue: 1, 8 - 15, 09.07.2021

Mohd. Danish Sıddıqı

Abstract

In the present research paper we study * Ricci solitons with a physical interpretation of the notion of the vector field associated with * Ricci solitons. We investigate the geometrical symmetries of Petrov type D gravitational fields along the vector field also associated with * Ricci solitons.

Keywords

*Ricci solitons Petroy type D gravitational field Weyl curvature tensor

References

  • Ahsan Z. Symmetries of the Electromagnetic fields in General Relativity. Acta Phys. Sincia. 1995. 337 (4).
  • Ahsan Z. A Symmetry properties of the spacetime of general relativity in terms of the space matter tensor. Brazilin Journal of Phys. 1996. 26(3): 572-576.
  • Ahsan Z. Interacting radiation field. Indian J. Pure App. Maths. 2000. 31(2): 215-225.
  • Ahsan Z. On a geometrical symmetry of the spacetime of general relativity. Bull. Cal. Math. Soc. 2005.97 (3): 191-200.
  • Ali M, Ahsan, Z. Ricci Solitons and Symmetries of spacetime manifold of General relativity. Glob. J. Adv. Res. Class. Mod. Geom. 2013. 1(2): 75-84.
  • Ali M, Ahsan Z. Gravitational field of Schwarzschild soliton. Arab J. Math. SCI. Available from: http://dx.doi.org/10.1016/j/ajmsc.2013.10.003.
  • Akbar MM, Woolger E. Ricci soliton and Einstein scalar field theory. Class. Quantum Grav. 2009. 26, 55015.
  • B List. Evolution of an extended Ricci flow system, Phd thesis 2005.
  • Catino G, Mazzieri L. Gradient Einstein solitons. Nonlinear Analysis. 2016. 132: 66-74.
  • Davis WR, Green LH., Norris LK. Relativistic matter fields admitting Ricci collineation and elated conservation laws. II Nuovo Cimento. 1976. 34(B): 256-280.
  • Duggal KL. Relativistic fluids with shear and timelike conformal collineation. J. Math. Phys. 1987. 28: 2700-2705.
  • Katzin GH, Levine J. Application of Lie derivatives to the symmetries Geodesic mappings and first integrals in Riemannian spaces. J. Colloq. Math. 1972. 26: 21-38.
  • Norris LK, Green LH, Davis WR. Fluid space-time including electromagnetic fields admitting symmetry mappings belonging to the family of contracted Ricci collineations. J. Math. Phys. 1977. 18: 1305-1312.
  • Stepanov SE, Shelepova VN. A note on Ricci solitons. Mathmaticheskie Zametici. 2009. 86(3): 474-477.
  • Stephani H, Krammer, D, McCallum M, Herlt, E. Exact solutions of Einstein field equations. Cambridge Univ. Press, Cambridge; 2003.
  • Yano K. The theory of Lie derivative and its Application, Vol III, North Holand publishing co. Amsterdom p. Noordhoff L.T.D. Groningen; 1957.
  • Tachibana S. On almost-analytic vectors in almost-Kahlerian manifolds. Tohoku Math. J. 1959. 11(2): 247-265.
  • Kaimakamis G, Panagiotidou K. *Ricci solitons of real hypersurfaces in non-at complex space forms. J. Geom. Phys. 2014. 86: 408-413.

* Ricci Solitons and Symmetries of Type D Gravitational Fields in Spacetime Manifolds

Year 2021, Volume: 2 Issue: 1, 8 - 15, 09.07.2021

Mohd. Danish Sıddıqı

Abstract

In the present research paper we study * Ricci solitons with a physical interpretation of the notion of the vector field associated with * Ricci solitons. We investigate the geometrical symmetries of Petrov type D gravitational fields along the vector field also associated with * Ricci solitons.

Keywords

*Ricci solitons Petroy type D gravitational field Weyl curvature tensor

References

  • Ahsan Z. Symmetries of the Electromagnetic fields in General Relativity. Acta Phys. Sincia. 1995. 337 (4).
  • Ahsan Z. A Symmetry properties of the spacetime of general relativity in terms of the space matter tensor. Brazilin Journal of Phys. 1996. 26(3): 572-576.
  • Ahsan Z. Interacting radiation field. Indian J. Pure App. Maths. 2000. 31(2): 215-225.
  • Ahsan Z. On a geometrical symmetry of the spacetime of general relativity. Bull. Cal. Math. Soc. 2005.97 (3): 191-200.
  • Ali M, Ahsan, Z. Ricci Solitons and Symmetries of spacetime manifold of General relativity. Glob. J. Adv. Res. Class. Mod. Geom. 2013. 1(2): 75-84.
  • Ali M, Ahsan Z. Gravitational field of Schwarzschild soliton. Arab J. Math. SCI. Available from: http://dx.doi.org/10.1016/j/ajmsc.2013.10.003.
  • Akbar MM, Woolger E. Ricci soliton and Einstein scalar field theory. Class. Quantum Grav. 2009. 26, 55015.
  • B List. Evolution of an extended Ricci flow system, Phd thesis 2005.
  • Catino G, Mazzieri L. Gradient Einstein solitons. Nonlinear Analysis. 2016. 132: 66-74.
  • Davis WR, Green LH., Norris LK. Relativistic matter fields admitting Ricci collineation and elated conservation laws. II Nuovo Cimento. 1976. 34(B): 256-280.
  • Duggal KL. Relativistic fluids with shear and timelike conformal collineation. J. Math. Phys. 1987. 28: 2700-2705.
  • Katzin GH, Levine J. Application of Lie derivatives to the symmetries Geodesic mappings and first integrals in Riemannian spaces. J. Colloq. Math. 1972. 26: 21-38.
  • Norris LK, Green LH, Davis WR. Fluid space-time including electromagnetic fields admitting symmetry mappings belonging to the family of contracted Ricci collineations. J. Math. Phys. 1977. 18: 1305-1312.
  • Stepanov SE, Shelepova VN. A note on Ricci solitons. Mathmaticheskie Zametici. 2009. 86(3): 474-477.
  • Stephani H, Krammer, D, McCallum M, Herlt, E. Exact solutions of Einstein field equations. Cambridge Univ. Press, Cambridge; 2003.
  • Yano K. The theory of Lie derivative and its Application, Vol III, North Holand publishing co. Amsterdom p. Noordhoff L.T.D. Groningen; 1957.
  • Tachibana S. On almost-analytic vectors in almost-Kahlerian manifolds. Tohoku Math. J. 1959. 11(2): 247-265.
  • Kaimakamis G, Panagiotidou K. *Ricci solitons of real hypersurfaces in non-at complex space forms. J. Geom. Phys. 2014. 86: 408-413.
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Mohd. Danish Sıddıqı This is me

Publication Date July 9, 2021
Submission Date June 2, 2021
Published in Issue Year 2021 Volume: 2 Issue: 1

Cite

APA Sıddıqı, M. D. (2021). * Ricci Solitons and Symmetries of Type D Gravitational Fields in Spacetime Manifolds. Bingöl Üniversitesi Teknik Bilimler Dergisi, 2(1), 8-15.
AMA Sıddıqı MD. * Ricci Solitons and Symmetries of Type D Gravitational Fields in Spacetime Manifolds. BUTS. July 2021;2(1):8-15.
Chicago Sıddıqı, Mohd. Danish. “* Ricci Solitons and Symmetries of Type D Gravitational Fields in Spacetime Manifolds”. Bingöl Üniversitesi Teknik Bilimler Dergisi 2, no. 1 (July 2021): 8-15.
EndNote Sıddıqı MD (July 1, 2021) * Ricci Solitons and Symmetries of Type D Gravitational Fields in Spacetime Manifolds. Bingöl Üniversitesi Teknik Bilimler Dergisi 2 1 8–15.
IEEE M. D. Sıddıqı, “* Ricci Solitons and Symmetries of Type D Gravitational Fields in Spacetime Manifolds”, BUTS, vol. 2, no. 1, pp. 8–15, 2021.
ISNAD Sıddıqı, Mohd. Danish. “* Ricci Solitons and Symmetries of Type D Gravitational Fields in Spacetime Manifolds”. Bingöl Üniversitesi Teknik Bilimler Dergisi 2/1 (July 2021), 8-15.
JAMA Sıddıqı MD. * Ricci Solitons and Symmetries of Type D Gravitational Fields in Spacetime Manifolds. BUTS. 2021;2:8–15.
MLA Sıddıqı, Mohd. Danish. “* Ricci Solitons and Symmetries of Type D Gravitational Fields in Spacetime Manifolds”. Bingöl Üniversitesi Teknik Bilimler Dergisi, vol. 2, no. 1, 2021, pp. 8-15.
Vancouver Sıddıqı MD. * Ricci Solitons and Symmetries of Type D Gravitational Fields in Spacetime Manifolds. BUTS. 2021;2(1):8-15.
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