Pluriclosed flow and Hermitian-symplectic structures

TL;DR

This paper investigates the behavior of pluriclosed flow on Hermitian-symplectic structures, revealing preservation properties, a modified flow with additional equations, and topological obstructions to long-term solutions.

Contribution

It demonstrates that pluriclosed flow preserves Hermitian-symplectic structures and introduces a flow of these forms with an extra evolution equation, providing new insights into their dynamics.

Findings

Pluriclosed flow preserves Hermitian-symplectic structures.

A modified flow with an extra Bismut-Ricci based equation is proposed.

Topological obstructions to long-time existence are identified.

Abstract

We show pluriclosed flow preserves the Hermitian-symplectic structures. And we observe that it can actually become a flow of Hermitian-symplectic forms when an extra evolution equation determined by the Bismut-Ricci form is considered. Moreover, we get a topological obstruction to the long-time existence in arbitrary dimension.