Quasi-convergence of the Ricci flow on locally homogeneous closed 4-manifolds

TL;DR

This paper investigates how certain families of metrics on locally homogeneous closed 4-manifolds evolve under Ricci flow, focusing on their quasi-convergence behavior and classifying equivalence classes.

Contribution

It introduces a framework for analyzing quasi-convergence of metrics on 4-manifolds and determines the dimensions of equivalence classes under specific conditions.

Findings

Identifies conditions for quasi-convergence of metrics.

Classifies the dimension of equivalence classes.

Provides insights into Ricci flow behavior on 4-manifolds.

Abstract

We study the quasi-convergence equivalence of some families of metrics on locally homogeneous closed 4-manifolds with trivial isotropy group, and identify the dimension of each equivalence class under certain conditions.