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

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.

Keywords

• Lorentzian Bianchi-Cartan-Vranceanu spaces
• Lorentzian metric
• Ricci solitons

References

1. Baird, P., Danielo, L., Three-dimensional Ricci solitons which project to surfaces, J. Reine Angew. Math., 608(2007), 65–91.
2. Batat,W., Sukilovic, T., Vukmirovic, S., Ricci solitons of three-dimensional Bianchi-Cartan-Vranceanu spaces, J. Geom., 111(1)(2020), 1–10.
3. Batat, W., Onda, K., Algebraic Ricci solitons of three-dimensional Lorentzian Lie groups, J. Geo. Phys., 114(2017), 138–152.
4. Cao, H.D., Geometry of Ricci solitons, Chinese Ann. Math. Ser. B, 27B(2006), 121–142.
5. Chow, B., Knopf, D., The Ricci Flow: An Introduction, Mathematical Surveys and Monographs, 110, American Mathematical Society, Providence, 2004.
6. 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.
7. Jablonski, M., Homogenous Ricci solitons, J. Reine Angew. Math.,699(2015), 159–182.
8. Lee, J.E., Slant curves in contact Lorentzian manifolds with CR structures, Mathematics, 8(1)(2020), 46.

9. Lee, J.E., Biharmonic curves in 3-dimensional Lorentzian-Sasakian space forms, Comm. Korean Math. Soc., 35(3)(2020), 967–977.
10. Onda, K., Lorentz Ricci solitons on 3-dimensional Lie groups, Geom. Dedicata, 147(2010), 313–322.
11. Sardar, A., Khan, M.N.I., De, U.C., h-*-Ricci solitons and almost co-K¨ahler manifolds, Mathematics, 9(24)(2021), 3200.
12. 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.
13. Yildirim, A., Slant curve in Lorentzian BCV spaces, J. Geo. Symm. Phys., 56(2020), 67–85.
14. Yildirim, A., On Lorentzian BCV spaces, Int. J. Math. Archive, 3(4)(2012), 1365–1371.