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

TL;DR

This paper classifies algebraic solitons for geometric evolution equations on three-dimensional Lie groups, focusing on cross curvature flow and renormalization group flow, revealing their relationship with soliton metrics.

Contribution

It provides a complete classification of left invariant algebraic solitons on simply connected three-dimensional unimodular Lie groups, linking algebraic and geometric soliton concepts.

Findings

Classification of algebraic solitons for specific flows

Relationship established between algebraic and soliton metrics

Complete characterization on three-dimensional unimodular 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.