We classify four dimensional homogeneous manifolds satisfying some generalized Einstein conditions. 1 4 ρ 2 g) and (M, g) is not Einstein.

Solitons for the two-loop renormalization group flow are studied in the four-dimensional homogeneous setting, providing a classification of algebraic steady four-dimensional solitons.

No abstract

No abstract

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.