Geodesic
Conformally Flat Algebraic Ricci Solitons on Lie Groups
Matematičeskie zametki, Tome 104 (2018) no. 1, pp. 62-73

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The paper is devoted to the study of conformally flat Lie groups with left-invariant (pseudo) Riemannian metric of an algebraic Ricci soliton. Previously conformally flat algebraic Ricci solitons on Lie groups have been studied in the case of small dimension and under an additional diagonalizability condition on the Ricci operator. The present paper continues these studies without the additional requirement that the Ricci operator be diagonalizable. It is proved that any nontrivial conformally flat algebraic Ricci soliton on a Lie group must be steady and have Ricci operator of Segrè type $\{(1\,\dots 1\,2)\}$ with a unique eigenvalue (equal to 0).
Keywords: metric Lie group, conformally flat (pseudo) Riemannian metric
Mots-clés : algebraic Ricci soliton. 
@article{MZM_2018_104_1_a6,
     author = {P. N. Klepikov},
     title = {Conformally {Flat} {Algebraic} {Ricci} {Solitons} on {Lie} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {62--73},
     publisher = {mathdoc},
     volume = {104},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_1_a6/}
}
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P. N. Klepikov. Conformally Flat Algebraic Ricci Solitons on Lie Groups. Matematičeskie zametki, Tome 104 (2018) no. 1, pp. 62-73. http://geodesic.mathdoc.fr/item/MZM_2018_104_1_a6/