This paper presents a complete classification of conformal Ricci collineations (CRCs) associated with the Bott connection on three-dimensional Lorentzian Lie groups. For each of the seven distinct classes of such groups, we derive explicit conditions under which left-invariant vector fields define CRCs, and we characterize the corresponding solution spaces. Specifically, we find that groups $ G_{1} $ and $ G_{7} $ admit rich non-trivial CRCs associated with $ \nabla^{B_{1}} $, highlighting the rich geometric structure induced by this connection.
Citation: Jinguo Jiang, Yanni Yang. On conformal Ricci collineations associated with the Bott connection on three-dimensional Lorentzian Lie groups[J]. Electronic Research Archive, 2026, 34(5): 3166-3192. doi: 10.3934/era.2026143
This paper presents a complete classification of conformal Ricci collineations (CRCs) associated with the Bott connection on three-dimensional Lorentzian Lie groups. For each of the seven distinct classes of such groups, we derive explicit conditions under which left-invariant vector fields define CRCs, and we characterize the corresponding solution spaces. Specifically, we find that groups $ G_{1} $ and $ G_{7} $ admit rich non-trivial CRCs associated with $ \nabla^{B_{1}} $, highlighting the rich geometric structure induced by this connection.
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Jinguo Jiang, Yanni Yang. On conformal Ricci collineations associated with the Bott connection on three-dimensional Lorentzian Lie groups[J]. Electronic Research Archive, 2026, 34(5): 3166-3192. doi: 10.3934/era.2026143
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