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Mat. Zametki, 2018, Volume 104, Issue 1, Pages 62–73 (Mi mz11758)  

Conformally Flat Algebraic Ricci Solitons on Lie Groups

P. N. Klepikov

Altai State University, Barnaul

Abstract: 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 $\{(1 …1 2)\}$ with a unique eigenvalue (equal to 0).

Keywords: metric Lie group, conformally flat (pseudo) Riemannian metric, algebraic Ricci soliton.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-31-00033 мол_а
This work was supported by the Russian Foundation for Basic Research under grant 18-31-00033 mol_a.


DOI: https://doi.org/10.4213/mzm11758

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English version:
Mathematical Notes, 2018, 104:1, 53–62

Bibliographic databases:

UDC: 514.765
Received: 28.07.2017

Citation: P. N. Klepikov, “Conformally Flat Algebraic Ricci Solitons on Lie Groups”, Mat. Zametki, 104:1 (2018), 62–73; Math. Notes, 104:1 (2018), 53–62

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