Geodesic
Invariant Ricci solitons on three-dimensional nonunimodular Lie groups with a left-invariant Lorentzian metric and a semisymmetric connection
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 48-61

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we investigate invariant Ricci solitons on three-dimensional nonunimodular metric Lie groups with a semisymmetric connection. We have proved that there exist nontrivial invariant Ricci solitons on some three-dimensional Lie groups with a left-invariant Lorentzian metric and a semisymmetric non Levi-Civita connection. Moreover a complete classification of nontrivial invariant Ricci solitons and the corresponding semisymmetric connections on three-dimensional nonunimodular Lie groups is obtained. In result we have given an answer on L.Cerbo conjecture about nontrivial invariant Ricci solitons.
Mots-clés : invariant Ricci solitons
Keywords: Lie groups, left-invariant Lorentzian metrics, semisymmetric connections. 
@article{SEMR_2023_20_1_a17,
     author = {P. N. Klepikov and E. D. Rodionov and O. P. Khromova},
     title = {Invariant {Ricci} solitons on three-dimensional nonunimodular {Lie} groups with a left-invariant {Lorentzian} metric and a semisymmetric connection},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {48--61},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_1_a17/}
}
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P. N. Klepikov; E. D. Rodionov; O. P. Khromova. Invariant Ricci solitons on three-dimensional nonunimodular Lie groups with a left-invariant Lorentzian metric and a semisymmetric connection. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 48-61. http://geodesic.mathdoc.fr/item/SEMR_2023_20_1_a17/