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Ricci Solitons of Three-Dimensional Lorentzian Bianchi-Cartan-Vranceanu Spaces

Year 2023, Volume: 15 Issue: 2, 270 - 276, 31.12.2023
https://doi.org/10.47000/tjmcs.1126267

Abstract

In this paper, we obtain explicit formulae for homogenous Ricci solitons on three-dimensional Lorentzian Bianchi-Cartan-Vranceanu spaces. We also give a result about Ricci solitons on a three dimensional Minkowski space.

References

  • Baird, P., Danielo, L., Three-dimensional Ricci solitons which project to surfaces, J. Reine Angew. Math., 608(2007), 65–91.
  • Batat,W., Sukilovic, T., Vukmirovic, S., Ricci solitons of three-dimensional Bianchi-Cartan-Vranceanu spaces, J. Geom., 111(1)(2020), 1–10.
  • Batat, W., Onda, K., Algebraic Ricci solitons of three-dimensional Lorentzian Lie groups, J. Geo. Phys., 114(2017), 138–152.
  • Cao, H.D., Geometry of Ricci solitons, Chinese Ann. Math. Ser. B, 27B(2006), 121–142.
  • Chow, B., Knopf, D., The Ricci Flow: An Introduction, Mathematical Surveys and Monographs, 110, American Mathematical Society, Providence, 2004.
  • Haseeb, A., Bilal, M., Chaubey, S.K., Khan, M.N.I., Geometry of indefinite Kenmotsu manifolds as *eta-Ricci-Yamabe solitons, Axioms, 11(9)(2022), 461.
  • Jablonski, M., Homogenous Ricci solitons, J. Reine Angew. Math.,699(2015), 159–182.
  • Lee, J.E., Slant curves in contact Lorentzian manifolds with CR structures, Mathematics, 8(1)(2020), 46.
  • Lee, J.E., Biharmonic curves in 3-dimensional Lorentzian-Sasakian space forms, Comm. Korean Math. Soc., 35(3)(2020), 967–977.
  • Onda, K., Lorentz Ricci solitons on 3-dimensional Lie groups, Geom. Dedicata, 147(2010), 313–322.
  • Sardar, A., Khan, M.N.I., De, U.C., h-*-Ricci solitons and almost co-K¨ahler manifolds, Mathematics, 9(24)(2021), 3200.
  • Vazquez, M.B., Calvaruso, G., Garc,a-Ri E., Gavino-Fern´andez, S., Three-dimensional Lorentzian homogeneous Ricci solitons, Isr. J. Math., 188(2012), 385–403.
  • Yildirim, A., Slant curve in Lorentzian BCV spaces, J. Geo. Symm. Phys., 56(2020), 67–85.
  • Yildirim, A., On Lorentzian BCV spaces, Int. J. Math. Archive, 3(4)(2012), 1365–1371.
Year 2023, Volume: 15 Issue: 2, 270 - 276, 31.12.2023
https://doi.org/10.47000/tjmcs.1126267

Abstract

References

  • Baird, P., Danielo, L., Three-dimensional Ricci solitons which project to surfaces, J. Reine Angew. Math., 608(2007), 65–91.
  • Batat,W., Sukilovic, T., Vukmirovic, S., Ricci solitons of three-dimensional Bianchi-Cartan-Vranceanu spaces, J. Geom., 111(1)(2020), 1–10.
  • Batat, W., Onda, K., Algebraic Ricci solitons of three-dimensional Lorentzian Lie groups, J. Geo. Phys., 114(2017), 138–152.
  • Cao, H.D., Geometry of Ricci solitons, Chinese Ann. Math. Ser. B, 27B(2006), 121–142.
  • Chow, B., Knopf, D., The Ricci Flow: An Introduction, Mathematical Surveys and Monographs, 110, American Mathematical Society, Providence, 2004.
  • Haseeb, A., Bilal, M., Chaubey, S.K., Khan, M.N.I., Geometry of indefinite Kenmotsu manifolds as *eta-Ricci-Yamabe solitons, Axioms, 11(9)(2022), 461.
  • Jablonski, M., Homogenous Ricci solitons, J. Reine Angew. Math.,699(2015), 159–182.
  • Lee, J.E., Slant curves in contact Lorentzian manifolds with CR structures, Mathematics, 8(1)(2020), 46.
  • Lee, J.E., Biharmonic curves in 3-dimensional Lorentzian-Sasakian space forms, Comm. Korean Math. Soc., 35(3)(2020), 967–977.
  • Onda, K., Lorentz Ricci solitons on 3-dimensional Lie groups, Geom. Dedicata, 147(2010), 313–322.
  • Sardar, A., Khan, M.N.I., De, U.C., h-*-Ricci solitons and almost co-K¨ahler manifolds, Mathematics, 9(24)(2021), 3200.
  • Vazquez, M.B., Calvaruso, G., Garc,a-Ri E., Gavino-Fern´andez, S., Three-dimensional Lorentzian homogeneous Ricci solitons, Isr. J. Math., 188(2012), 385–403.
  • Yildirim, A., Slant curve in Lorentzian BCV spaces, J. Geo. Symm. Phys., 56(2020), 67–85.
  • Yildirim, A., On Lorentzian BCV spaces, Int. J. Math. Archive, 3(4)(2012), 1365–1371.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Murat Altunbaş 0000-0002-0371-9913

Publication Date December 31, 2023
Published in Issue Year 2023 Volume: 15 Issue: 2

Cite

APA Altunbaş, M. (2023). Ricci Solitons of Three-Dimensional Lorentzian Bianchi-Cartan-Vranceanu Spaces. Turkish Journal of Mathematics and Computer Science, 15(2), 270-276. https://doi.org/10.47000/tjmcs.1126267
AMA Altunbaş M. Ricci Solitons of Three-Dimensional Lorentzian Bianchi-Cartan-Vranceanu Spaces. TJMCS. December 2023;15(2):270-276. doi:10.47000/tjmcs.1126267
Chicago Altunbaş, Murat. “Ricci Solitons of Three-Dimensional Lorentzian Bianchi-Cartan-Vranceanu Spaces”. Turkish Journal of Mathematics and Computer Science 15, no. 2 (December 2023): 270-76. https://doi.org/10.47000/tjmcs.1126267.
EndNote Altunbaş M (December 1, 2023) Ricci Solitons of Three-Dimensional Lorentzian Bianchi-Cartan-Vranceanu Spaces. Turkish Journal of Mathematics and Computer Science 15 2 270–276.
IEEE M. Altunbaş, “Ricci Solitons of Three-Dimensional Lorentzian Bianchi-Cartan-Vranceanu Spaces”, TJMCS, vol. 15, no. 2, pp. 270–276, 2023, doi: 10.47000/tjmcs.1126267.
ISNAD Altunbaş, Murat. “Ricci Solitons of Three-Dimensional Lorentzian Bianchi-Cartan-Vranceanu Spaces”. Turkish Journal of Mathematics and Computer Science 15/2 (December 2023), 270-276. https://doi.org/10.47000/tjmcs.1126267.
JAMA Altunbaş M. Ricci Solitons of Three-Dimensional Lorentzian Bianchi-Cartan-Vranceanu Spaces. TJMCS. 2023;15:270–276.
MLA Altunbaş, Murat. “Ricci Solitons of Three-Dimensional Lorentzian Bianchi-Cartan-Vranceanu Spaces”. Turkish Journal of Mathematics and Computer Science, vol. 15, no. 2, 2023, pp. 270-6, doi:10.47000/tjmcs.1126267.
Vancouver Altunbaş M. Ricci Solitons of Three-Dimensional Lorentzian Bianchi-Cartan-Vranceanu Spaces. TJMCS. 2023;15(2):270-6.