Generalized Ricci Solitons of Four-Dimensional Non-Abelian Nilpotent Lie Groups

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2025年7月3日

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Jinguo Jiang,
Yanni Yang

摘要

In this work, we investigate generalized Ricci solitons on four-dimensional non-Abelian Lie groups and undertake a comprehensive classification of left-invariant affine generalized Ricci solitons equipped with left-invariant Lorentzian metrics. Also, we derive that four-dimensional non-Abelian nilpotent Lie groups with left-invariant Lorentzian metric have non-trivial Killing vector fields except for \((G_{4},g_{2}^{\lambda })\) . Furthermore, both \((G_{4},g_{1}^{\lambda })\) and \((G_{4},g_{2}^{\lambda })\) admit non-trivial homogeneous Ricci solitons.