# An almost complex Chern-Ricci flow

## TL;DR

This paper studies an evolution equation for almost Hermitian metrics driven by the Chern-Ricci form, extending known flows to non-integrable almost complex structures and analyzing its existence and convergence properties.

## Contribution

It introduces and analyzes the almost complex Chern-Ricci flow, generalizing classical flows to almost complex manifolds and providing maximal existence time and convergence results.

## Key findings

- Maximal existence time characterized by initial data
- Flow converges under certain conditions
- Detailed analysis on homogeneous manifolds

## Abstract

We consider the evolution of an almost Hermitian metric by the $(1,1)$ part of its Chern-Ricci form on almost complex manifolds. This is an evolution equation first studied by Chu and coincides with the Chern-Ricci flow if the complex structure is integrable and with the K\"ahler-Ricci flow if moreover the initial metric is K\"ahler. We find the maximal existence time for the flow in term of the initial data and also give some convergence results. As an example, we study this flow on the (locally) homogeneous manifolds in more detail.