# Hermitian Curvature Flow on compact homogeneous spaces

## TL;DR

This paper investigates the Hermitian curvature flow on compact homogeneous complex manifolds, analyzing its finite-time extinction, invariant static metrics, and convergence behavior of the normalized flow.

## Contribution

It introduces a study of the Hermitian curvature flow on these manifolds, including extinction time, static metrics, and flow convergence analysis.

## Key findings

- Flow has finite extinction time T>0
- Identifies invariant static metrics
- Normalized flow converges to static metrics

## Abstract

We study a version of the Hermitian curvature flow on compact homogeneous complex manifolds. We prove that the solution has a finite exstinction time $T>0$ and we analyze its behaviour when $t\to T$. We also determine the invariant static metrics and we study the convergence of the normalized flow to one of them.