Invariant Ricci solitons on three-dimensional nonunimodular Lie groups with a left-invariant Lorentzian metric and a semisymmetric connection

In this paper we investigate invariant Ricci solitons on three-dimensional nonunimodular metric Lie groups with a semisymmetric connection. We have proved that there exist nontrivial invariant Ricci solitons on some three-dimensional Lie groups with a left-invariant Lorentzian metric and a semisymmetric non Levi-Civita connection. Moreover a complete classification of nontrivial invariant Ricci solitons and the corresponding semisymmetric connections on three-dimensional nonunimodular Lie groups is obtained. In result we have given an answer on L.Cerbo conjecture about nontrivial invariant Ricci solitons.