* 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.