The solvmanifold conjecture for expanding homogeneous Ricci solitons

An expanding homogeneous Ricci soliton is a homogeneous Ricci soliton with soliton constant $\lambda<0$. A solvmanifold is a homogeneous space associated with a solvable Lie group; “simply-connected” has its usual topological meaning. The solvmanifold conjecture for expanding homogeneous Ricci solitons. Every expanding homogeneous Ricci soliton is isometric to a simply-connected solvmanifold.

This conjecture would constrain the possible expanding homogeneous Ricci solitons and is presented as a step toward understanding the Type-III asymptotic-soliton conjecture. Its resolution is not given in the supplied text.