In this paper, we defined affine Yano–Ricci solitons and perturbed Yano–Ricci solitons on three-dimensional Lorentzian Lie groups and obtain their complete classification. The major results indicated that all groups $ G_{3}, \cdots, G_{7} $ admit both affine Yano–Ricci solitons and their perturbed companions, whereas $ G_{1} $ supports neither. As a corollary, we found that the Lorentzian Lie groups $ G_{3}, G_{5} $, and $ G_{6} $ are affine Einstein manifolds with respect to the Yano connection.
Citation: Jiajing Miao, Xinrui Li, Haiming Liu. Affine Yano and perturbed Yano–Ricci solitons on Lorentzian Lie groups[J]. Electronic Research Archive, 2026, 34(5): 3554-3572. doi: 10.3934/era.2026159
In this paper, we defined affine Yano–Ricci solitons and perturbed Yano–Ricci solitons on three-dimensional Lorentzian Lie groups and obtain their complete classification. The major results indicated that all groups $ G_{3}, \cdots, G_{7} $ admit both affine Yano–Ricci solitons and their perturbed companions, whereas $ G_{1} $ supports neither. As a corollary, we found that the Lorentzian Lie groups $ G_{3}, G_{5} $, and $ G_{6} $ are affine Einstein manifolds with respect to the Yano connection.
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Jiajing Miao, Xinrui Li, Haiming Liu. Affine Yano and perturbed Yano–Ricci solitons on Lorentzian Lie groups[J]. Electronic Research Archive, 2026, 34(5): 3554-3572. doi: 10.3934/era.2026159
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