Ricci bi-conformal vector fields on Lorentzian five-dimensional two-step nilpotent Lie groups

Year 2024, , 1118 - 1129, 27.08.2024

Shahroud Azami , U.c. De

https://doi.org/10.15672/hujms.1294973

Abstract

In this paper, we completely classify Ricci bi-conformal vector fields on simply-connected five-dimensional two-step nilpotent Lie groups which are also connected and we show which of them are the Killing vector fields and gradient vector fields.

Keywords

Ricci bi-conformal vector fields, pseudo-Riemannian metrics, nilpotent Lie group

References

• [1] S. Azami, Generalized Ricci solitons of three-dimensional Lorentzian Lie groups associated canonical connections and Kobayashi-Nomizu connections, J. Nonlinear Math. Phys. 30 (1), 1-33, 2023.
• [2] P. Baird and L. Danielo, Three-dimensional Ricci solitons whichproject to surfaces, J. Reine Angew. Math. 608, 65-91, 2007.
• [3] W. Batat and K. Onda, Four-dimensional pseudo-Riemannian generalized symmetric spaces which are algebraic Ricci solitons, Results Math. 64, 253-267, 2013.
• [4] N. Bokan, T. Sukilovic and S. Vukmirovic, Lorentz geometry of 4-dimensional nilpotent Lie groups, Geom. dedicata 177, 83-102, 2015.
• [5] A. Bouharis and B. Djebbar, Ricci solitons on Lorentzian four-dimensional generalized symmetric spaces, J. Math. Phys. Anal. Geom. 14 (2), 132-140, 2018.
• [6] G. Calvaruso, Three-dimensional homogeneous generalized Ricci solitons, Mediterr. J. Math. 14 (5), 1-21, 2017.
• [7] S. M. Carroll, Spacetime and geometry: an introduction to general relativity, Addison Wesley., 133-139, 2004.
• [8] B. Coll, S. R. Hldebrondt and J. M. M. Senovilla, Kerr-Schild symmetries, Gen. Relativ. Gravit. 33, 649-670, 2001.
• [9] 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.
• [10] S. Deshmukh, Geometry of conformal vector fields, Arab. J. Math. 23 (1), 44-73, 2017.
• [11] A. Garcia-Parrado and J. M. M. Senovilla, Bi-conformal vector fields and their applications, Classical Quantum Gravity 21 (8), 2153-2177, 2004.
• [12] R. S. Hamilton, The Ricci flow on surfaces in Mathematics and General Relativity, Contemps. Math. 71, Amer. Math. Soc. Providence, RI, 1988, 237-262.
• [13] J. Lauret, Ricci solitons solvmanifolds, J. Reine Angew. Math. 650, 1-21, 2011.
• [14] L. Magnin, Sue les algébres de Lie nilpotents de dimension$\leq7$, J. Geom. Phys. 3 (1), 119, 1986.
• [15] P. Nurowski and M. Randall, Generalized Ricci solitons, J. Geom. Anal. 26, 1280- 1345, 2016.
• [16] T. H. Wears, On Lorentzian Ricci solitons on nilpotent Lie groups, Math. Nachr. 290 (8-9), 1381-1405, 2017.
• [17] K. Yano, The theory of Lie derivatives and its applications, Dover publications, 2020.