Abstract
Homogeneous Ricci solitons on four-dimensional Lie groups with a left-invariant Riemannian metric are studied. The absence of nontrivial homogeneous invariant Ricci solitons is proved. The algebraic soliton equations are solved in terms of the structure constants of the metric Lie algebra.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. L. Besse, Einstein Manifolds (Springer, Berlin, 1987; Mir, Moscow, 1990), Vol. 1.
Yu. G. Nikonorov, E. D. Rodionov, and V. V. Slavskii, J. Math. Sci. 146 (6), 6313–6390 (2007).
M. Wang, Suppl. J. Differ. Geom. 6, 287–325 (1999).
R. S. Hamilton, Contemp. Math. 71, 237–261 (1988).
L. D. Cerbo, Adv. Geom. 14 (2), 225–237 (2014).
G. M. Mubarakzyanov, Izv. Vyssh. Uchebn. Zaved., Mat. 32 (1), 144 (1963).
P. N. Klepikov and D. N. Oskorbin, Izv. Altaisk. Univ. 85 (1), 75–78 (2015).
I. V. Arzhantsev, Gröbner Bases and Systems of Algebraic Equations (MTsNMO, Moscow, 2003) [in Russian].
J. Lauret, J. Reine Angew. Math. 650, 1–21 (2011).
O. P. Gladunova, E. D. Rodionov, and V. V. Slavskii, Vladikavk. Mat. Zh. 13 (3), 3–16 (2011).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © P.N. Klepikov, D.N. Oskorbin, E.D. Rodionov, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 3, pp. 281–283.
Rights and permissions
About this article
Cite this article
Klepikov, P.N., Oskorbin, D.N. & Rodionov, E.D. Homogeneous Ricci solitons on four-dimensional Lie groups with a left-invariant Riemannian metric. Dokl. Math. 92, 701–703 (2015). https://doi.org/10.1134/S1064562415060150
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064562415060150