Pluriclosed Flow and Hermitian-Symplectic Structures

We observe that pluriclosed flow preserves Hermitian-symplectic structures. And we extend pluriclosed flow to a flow of Hermitian-symplectic forms by adding an extra evolution equation, which is determined by the (2, 0)-part of Bismut–Ricci form. Moreover, we obtain a topological obstruction to the existence of global solutions in every dimension.