The behavior of the second Ricci flow on complex parallelizable manifolds

TL;DR

This paper investigates the second Chern-Ricci flow on compact complex parallelizable manifolds, establishing regularity results and demonstrating the stability of Chern-flat metrics within this geometric flow context.

Contribution

It provides new regularity results for the second Chern-Ricci flow and proves the dynamic stability of Chern-flat metrics on complex parallelizable manifolds.

Findings

Regularity results for the flow on compact complex parallelizable manifolds

Proof of the stability of Chern-flat metrics under the flow

Insights into Hermitian curvature flows and their geometric implications

Abstract

We study the flow of Hermitian metrics governed by the second Chern-Ricci form on a compact complex manifolds. The flow belongs to the family of Hermitian curvature flows introduced by Streets and Tian and it was considered by Lee in order to study compact Hermitian manifolds with almost negative Chern bisectional curvature. We show a regularity result on compact complex parallelizable manifolds and we prove that Chern-flat metrics are dynamically stable.