The relationship between algebraic soliton metrics and self-similar solutions of geometric evolution equations on Lie groups is investigated. After discussing the general relationship between algebraic soliton metrics and self-similar solutions to geometric evolution equations, we investigate the cross curvature flow and the second order renormalization group flow on simply-connected, three-dimensional, unimodular Lie groups, providing a complete classification of left invariant algebraic solitons that give rise to self-similar solutions of the corresponding flows on such spaces.
"On algebraic solitons for geometric evolution equations on three-dimensional Lie groups." Tbilisi Math. J. 9 (2) 33 - 58, December 2016. https://doi.org/10.1515/tmj-2016-0018