On algebraic solitons for geometric evolution equations on three-dimensional Lie groups

Abstract

In this paper, we investigate the relationship between algebraic soliton metrics and soliton metrics for geometric evolution equations on Lie groups. After discussing the general relationship between algebraic soliton metrics and soliton metrics, 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 on such spaces.