Ricci bi-conformal vector fields on four-dimensional Lorentzian Damek-Ricci spaces
DOI:
https://doi.org/10.5269/bspm.67903Abstract
In this paper, we obtain all Ricci bi-conformal vector fields on the four-dimensional Lorentzian Damek-Ricci spaces and we show that four-dimensional Lorentzian Damek-Ricci spaces have not nontrivial Ricci bi-conformal vector fields as gradient vector filed. Also, we determine which of them are Killing vector fields.
References
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14. N. Sidhoumi, Ricci solitons of four-dimensional Lorentzian Damek–Ricci spaces, Journal of Mathematical Physics, Analysis, Geometry, 16(2), 190-199, (2020).
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2. J. Berndt, F. Tricerri, and L. Vanhecke, Generalized Heisenberg Groups and Damek- Ricci Harmonic Spaces, Lect. Notes Math., 1598, Springer, Heidelberg, 1995.
3. J. Carlos D´Ä±az-Ramos and M. Domınguez-Vazquez, Isoparametric hypersurfaces in Damek-Ricci spaces, Adv. Math. 239, 1-17, (2013).
4. S. M. Carroll, Spacetime and Geometry: An Introduction to General Relativity, Addison Wesley. 133-139, (2004).
5. A. Cintra, F. Mercuri, and I. Onnis, Minimal surfaces in 4-dimensional Lorentzian Damek-Ricci spaces, preprint, https://arxiv.org/abs/math/1501.03427, (2015).
6. B. Coll, S. R. Hldebrondt and J. M. M. Senovilla, Kerr-Schild symmetries, General relativity and gravitation, 33, 649-670, (2001).
7. E. Damek and F. Ricci, A Class of nonsymmetric Harmonic Riemannian spaces, Bulletin Amer. Math. Soc. 27, 139-142, (1992).
8. U. C. De, A. Sardar, and A. Sarkar, Some conformal vector fields and conformal Ricci solitons on N(k)-contact metric manifolds, AUT J. Math. Com., 2 (1), 61-71, (2021).
9. S. Degla and L. Todjihounde, Biharmonic curve in four-dimensional Damek-Ricci spaces, J. Math. Sci.: Adv. Appl. 5, 19-27, (2010).
10. S. Deshmukh, Geometry of Conformal Vector Fields, Arab. J. Math., 23(1), 44-73.
11. A. Garcia-Parrado and J. M. M. Senovilla, Bi-conformal vector fields and their applications, Classical and Quantum Gravity, 21 (8), 2153-2177, (2004).
12. M. Koivogui and L. Todjihounde, Weierstrass Representation for minimal immer- sions into Damek-Ricci spaces, Int. Electron. J. Geom. 6, 1-7, (2013).
13. A. Mostefaoui and N. Sidhoumi, Homogeneous structures on four-dimensional Lorentzian Damek-Ricci spaces, Commun. Korean Math. Soc., 38(1), 195-203, (2023).
14. N. Sidhoumi, Ricci solitons of four-dimensional Lorentzian Damek–Ricci spaces, Journal of Mathematical Physics, Analysis, Geometry, 16(2), 190-199, (2020).
15. J. Tan and S. Deng, Some geometrical properties of four dimensional Lorentzian Damek-Ricci spaces, Publ. Math. Debrecen 89, 105-124, (2016).
16. K. Yano, The theory of Lie derivatives and its applications, Dover publications, 2020.
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Published
2025-08-11
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How to Cite
Azami, S. (2025). Ricci bi-conformal vector fields on four-dimensional Lorentzian Damek-Ricci spaces. Boletim Da Sociedade Paranaense De Matemática, 43, 1-8. https://doi.org/10.5269/bspm.67903
