Perturbed Bott algebraic Schouten solitons on 3D Lorentzian Lie groups

Xinrui Li; Jiajing Miao; Haiming Liu; Xinrui Li; Jiajing Miao; Haiming Liu

doi:10.3934/era.2025339

Electronic Research Archive

2025, Volume 33, Issue 12: 7676-7698. doi: 10.3934/era.2025339

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Perturbed Bott algebraic Schouten solitons on 3D Lorentzian Lie groups

School of Mathematic Science, Mudanjiang Normal University, Mudanjiang 157011, China
† All authors contributed to this work equally and should be regarded as co-first authors.

Received: 28 October 2025 Revised: 17 December 2025 Accepted: 18 December 2025 Published: 22 December 2025

In this paper, we defined and classified the algebraic Schouten solitons that are associated with the perturbed Bott connection on three-dimensional Lorentzian Lie groups possessing three distinct distributions. By transforming equations of perturbed Bott algebraic Schouten solitons into algebraic equations, we found that $ G_3, G_5, G_6 $, and $ G_7 $ have perturbed Bott algebraic Schouten solitons under the first distribution. $ G_3, G_6 $, and $ G_7 $ have such solitons under the second distribution. Additionally, $ G_2, G_3, G_4, G_5, G_6 $, and $ G_7 $ have such solitons under the third distribution.
- algebraic Schouten solitons,
- perturbed Bott connection,
- Lorentzian Lie groups
Citation: Xinrui Li, Jiajing Miao, Haiming Liu. Perturbed Bott algebraic Schouten solitons on 3D Lorentzian Lie groups[J]. Electronic Research Archive, 2025, 33(12): 7676-7698. doi: 10.3934/era.2025339

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Abstract

In this paper, we defined and classified the algebraic Schouten solitons that are associated with the perturbed Bott connection on three-dimensional Lorentzian Lie groups possessing three distinct distributions. By transforming equations of perturbed Bott algebraic Schouten solitons into algebraic equations, we found that $ G_3, G_5, G_6 $, and $ G_7 $ have perturbed Bott algebraic Schouten solitons under the first distribution. $ G_3, G_6 $, and $ G_7 $ have such solitons under the second distribution. Additionally, $ G_2, G_3, G_4, G_5, G_6 $, and $ G_7 $ have such solitons under the third distribution.

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