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

Yıl 2024, Cilt: 53 Sayı: 4, 1118 - 1129, 27.08.2024
https://doi.org/10.15672/hujms.1294973

Öz

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.

Kaynakça

  • [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.
Yıl 2024, Cilt: 53 Sayı: 4, 1118 - 1129, 27.08.2024
https://doi.org/10.15672/hujms.1294973

Öz

Kaynakça

  • [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.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Shahroud Azami 0000-0002-8976-2014

U.c. De 0000-0002-8990-4609

Erken Görünüm Tarihi 10 Ocak 2024
Yayımlanma Tarihi 27 Ağustos 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 53 Sayı: 4

Kaynak Göster

APA Azami, S., & De, U. (2024). Ricci bi-conformal vector fields on Lorentzian five-dimensional two-step nilpotent Lie groups. Hacettepe Journal of Mathematics and Statistics, 53(4), 1118-1129. https://doi.org/10.15672/hujms.1294973
AMA Azami S, De U. Ricci bi-conformal vector fields on Lorentzian five-dimensional two-step nilpotent Lie groups. Hacettepe Journal of Mathematics and Statistics. Ağustos 2024;53(4):1118-1129. doi:10.15672/hujms.1294973
Chicago Azami, Shahroud, ve U.c. De. “Ricci Bi-Conformal Vector Fields on Lorentzian Five-Dimensional Two-Step Nilpotent Lie Groups”. Hacettepe Journal of Mathematics and Statistics 53, sy. 4 (Ağustos 2024): 1118-29. https://doi.org/10.15672/hujms.1294973.
EndNote Azami S, De U (01 Ağustos 2024) Ricci bi-conformal vector fields on Lorentzian five-dimensional two-step nilpotent Lie groups. Hacettepe Journal of Mathematics and Statistics 53 4 1118–1129.
IEEE S. Azami ve U. De, “Ricci bi-conformal vector fields on Lorentzian five-dimensional two-step nilpotent Lie groups”, Hacettepe Journal of Mathematics and Statistics, c. 53, sy. 4, ss. 1118–1129, 2024, doi: 10.15672/hujms.1294973.
ISNAD Azami, Shahroud - De, U.c. “Ricci Bi-Conformal Vector Fields on Lorentzian Five-Dimensional Two-Step Nilpotent Lie Groups”. Hacettepe Journal of Mathematics and Statistics 53/4 (Ağustos 2024), 1118-1129. https://doi.org/10.15672/hujms.1294973.
JAMA Azami S, De U. Ricci bi-conformal vector fields on Lorentzian five-dimensional two-step nilpotent Lie groups. Hacettepe Journal of Mathematics and Statistics. 2024;53:1118–1129.
MLA Azami, Shahroud ve U.c. De. “Ricci Bi-Conformal Vector Fields on Lorentzian Five-Dimensional Two-Step Nilpotent Lie Groups”. Hacettepe Journal of Mathematics and Statistics, c. 53, sy. 4, 2024, ss. 1118-29, doi:10.15672/hujms.1294973.
Vancouver Azami S, De U. Ricci bi-conformal vector fields on Lorentzian five-dimensional two-step nilpotent Lie groups. Hacettepe Journal of Mathematics and Statistics. 2024;53(4):1118-29.