Abstract
We give the classification of homogenous Ricci solitons on three-dimensional Bianchi–Cartan–Vranceanu spaces.
Similar content being viewed by others
References
Barros, A.B., Ribeiro, E.R., Silva Filho, J.: Uniqueness of quasi-Einstein metrics on 3-dimensional homogeneous manifolds. Differ. Geom. Appl. 35, 60–73 (2014)
Bianchi, L.: Gruppi continui e finiti. Ed. Zanichelli, Bologna (1928)
Brozos-Vázquez, M., Calvaruso, G., Garcia-Rio, E., Gavino-Fernández, S.: Three-dimensional Lorentzian homogeneous Ricci solitons. Israel J. Math. 188(1), 385–403 (2012)
Calvaruso, G.: Three-dimensional homogeneous generalized Ricci solitons. Mediterr. J. Math. 14(5), 216 (2017)
Cartan, É.: Leçons sur la géométrie des espaces de Riemann. Gauthier Villars, Paris (1946)
Di Cerbo, L.F.: Generic properties of homogeneous Ricci solitons. Adv. Geom. 14(2), 225–237 (2014)
Klepikov, P.N., Oskorbin, D.N.: Homogeneous invariant Ricci solitons on four-dimensional Lie groups. Izv. Altaisk. Univ. 85(1), 75–78 (2015)
Lafuente, R., Lauret, J.: On homogeneous Ricci solitons. Q. J. Math. 65, 399–419 (2014)
Lauret, J.: Ricci soliton homogeneous nilmanifolds. Math. Ann. 319, 715 (2001). https://doi.org/10.1007/PL00004456
Thurston, W.M.: Three dimensional geometry and topology I. Princeton Math Series, S., Levy, (ed) Vol. 35, Princeton University Press, Princeton (1997). https://www.amazon.com/Lecons-Geometrie-Differentielle-G-Vranceanu/dp/B000KFQWGG
Vranceanu, G.: Leçons de géométrie differentielle. Ed. Acad. Rep. Pop. Roum., vol. I, Bucarest (1957)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The second and third author were supported by funds of the project 174012 through the Ministry of Education and Science of the Republic of Serbia.
Rights and permissions
About this article
Cite this article
Batat, W., Šukilović, T. & Vukmirović, S. Ricci solitons of three-dimensional Bianchi–Cartan–Vranceanu spaces. J. Geom. 111, 1 (2020). https://doi.org/10.1007/s00022-019-0515-x
Received:
Revised:
Published:
DOI: https://doi.org/10.1007/s00022-019-0515-x