# A scalar Calabi-type flow in Hermitian Geometry: Short-time existence and stability

## TL;DR

This paper introduces a new Hermitian geometric flow based on the second derivative of the Chern scalar curvature, proving short-time existence and stability under certain conditions, with implications for special Hermitian structures.

## Contribution

It presents a novel scalar Calabi-type flow for Hermitian metrics, establishing short-time existence and stability results, and analyzing its behavior relative to background metrics.

## Key findings

- Flow preserves balanced and Gauduchon metrics.
- Unique short-time solution exists for the flow.
- Stability proven when background metric is Kähler-Einstein with nonpositive scalar curvature.

## Abstract

We introduce a new geometric flow of Hermitian metrics which evolves an initial metric along the second derivative of the Chern scalar curvature. The flow depends on the choice of a background metric, it always reduces to a scalar equation and preserves some special classes of Hermitian structures, as balanced and Gauduchon metrics. We show that the flow has always a unique short-time solution and we provide a stability result when the background metric is Kaehler-Einstein with nonpositive scalar curvature.