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

Source abstract

Abstract 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.