# Geometric formalities along the Chern-Ricci flow

## TL;DR

This paper investigates how geometric formality concepts evolve under the Chern-Ricci flow on certain complex surfaces, providing insights into the interplay between geometric structures and complex geometric flows.

## Contribution

It extends the study of geometric formality to the Hermitian setting under the Chern-Ricci flow on class VII surfaces, including Hopf, Inoue, and Kodaira surfaces.

## Key findings

- Geometric formality notions evolve in specific ways under the flow.
- The study provides new understanding of complex surface geometry.
- Results highlight differences between various surface types.

## Abstract

In this paper, we study how the notions of geometric formality according to Kotschick and other geometric formalities adapted to the Hermitian setting evolve under the action of the Chern-Ricci flow on class VII surfaces, including Hopf and Inoue surfaces, and on Kodaira surfaces.