Affine Yano and perturbed Yano–Ricci solitons on Lorentzian Lie groups

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.