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

We determine all three-dimensional homogeneous and 1 -curvature homogeneous Lorentzian metrics which are critical for a quadratic curvature functional. As a result, we show that any quadratic curvature functional admits ...