# Remarks on Chern-Einstein Hermitian metrics

## TL;DR

This paper investigates properties and examples of Hermitian metrics on complex manifolds where the Chern curvature trace is proportional to the metric, contributing to the understanding of Chern-Einstein Hermitian metrics.

## Contribution

It provides new insights and examples of Chern-Einstein Hermitian metrics, enhancing the theoretical framework of such geometric structures.

## Key findings

- Identification of key properties of Chern-Einstein Hermitian metrics
- Construction of explicit examples illustrating these metrics
- Analysis of the implications for complex differential geometry

## Abstract

We study some basic properties and examples of Hermitian metrics on complex manifolds whose traces of the curvature of the Chern connection are proportional to the metric itself.