We determine all non-Einstein Ricci solitons on four-dimensional Lorentzian Lie groups whose soliton vector field is left-invariant. In addition to pp-wave and plane wave Lie groups, there are four families of Lorentzian ...

We classify homogeneous four-dimensional manifolds satisfying a curvature condition which naturally generalizes the Einstein one. Our work leads to new examples of self-similar solutions of the two-loop renormalization group flow