Geodesic
Invariant Ricci solitons on three-dimensional metric Lie groups with semi-symmetric connection
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2021), pp. 80-85.

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In this paper, we investigate invariant Ricci solitons, an important subclass in the class of homogeneous Ricci solitons. A classification of invariant Ricci solitons on three-dimensional Lie groups with a left-invariant Riemannian metric and a semi-symmetric connection different from the Levi–Civita connection is obtained. It is proved that in this case there exist invariant Ricci solitons with nonconformal Killing vector field.
Mots-clés : Invariant Ricci solitons
Keywords: left–invariant Riemannian metrics, Lie groups, semi-symmetric connections. 
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     author = {P. N. Klepikov and E. D. Rodionov and O. P. Khromova},
     title = {Invariant {Ricci} solitons on three-dimensional metric {Lie} groups with semi-symmetric connection},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
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P. N. Klepikov; E. D. Rodionov; O. P. Khromova. Invariant Ricci solitons on three-dimensional metric Lie groups with semi-symmetric connection. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2021), pp. 80-85. http://geodesic.mathdoc.fr/item/IVM_2021_8_a8/

[1] Cartan E., “Sur les variétés à connexion affine et la théorie de la relativité généralisée (deuxième partie)”, Ann. Ecole Norm. Sup., 42 (1925), 17–88 | DOI | MR | Zbl

[2] Yano K., “On semi-symmetric metric connection”, Revue Roumame de Math. Pure et Appl., 15 (1970), 1579–1586 | MR | Zbl

[3] Agricola I., Kraus M., “Manifolds with vectorial torsion”, Diff. Geom. and Appl., 46 (2016), 130–147 | DOI | MR

[4] Barua B., Ray A.Kr., “Some properties of a semi-symmetric metric connection in a Riemannian manifold”, Indian J. pure appl. Math., 16:7 (1985), 736–740 | MR | Zbl

[5] De U.C., De B.K., “Some properties of a semi-symmetric metric connection on a Riemannian manifold”, Istanbul Univ. Fen. Fak. Mat. Der., 54 (1995) | MR

[6] Cerbo L. F., “Generic properties of homogeneous Ricci solitons”, Adv. Geom., 14:1 (2014), 225–237 | DOI | MR | Zbl

[7] Klepikov P. N., Oskorbin D. N., “Odnorodnye invariantnye solitony Richchi na chetyrekhmernykh gruppakh Li”, Izv. AltGU, 85:1 (2015), 115–122

[8] Milnor J., “Curvatures of left invariant metrics on Lie groups”, Adv. Math., 21 (1976), 293–329 | DOI | MR | Zbl