The pluriclosed flow and the Vaisman condition

TL;DR

This paper investigates the behavior of the pluriclosed flow on compact complex surfaces, establishing that it preserves the Vaisman condition precisely when the initial metric has constant scalar curvature.

Contribution

It provides a characterization of when the pluriclosed flow preserves the Vaisman condition, linking it to the scalar curvature of the initial metric.

Findings

Pluriclosed flow preserves Vaisman condition under constant scalar curvature.

The preservation is an if and only if condition.

Initial scalar curvature determines flow behavior.

Abstract

We prove that the pluriclosed flow preserves the Vaisman condition on compact complex surfaces if and only if the starting metric has constant scalar curvature.