Invariant Ricci solitons on three-dimensional metric Lie groups with semi-symmetric connection

In this paper, we investigate invariant Ricci solitons, an important subclass in the class of homogeneous Ricci solitons. A classification of invariant Ricci solitons on three-dimensional Lie groups with a left-invariant Riemannian metric and a semi-symmetric connection different from the Levi–Civita connection is obtained. It is proved that in this case there exist invariant Ricci solitons with nonconformal Killing vector field.