The pluriclosed flow is an example of Hermitian flows generalizing the Kähler-Ricci flow. We classify static pluriclosed solutions of the pluriclosed flow on non-Kähler minimal compact complex surfaces. We show that there are no static pluriclosed metrics on Kodaira surfaces, non-Kähler minimal properly elliptic surfaces and Inoue surfaces.
"On the Non-existence of Static Pluriclosed Metrics on Non-Kähler Minimal Complex Surfaces." Tokyo J. Math. 41 (1) 65 - 76, June 2018. https://doi.org/10.3836/tjm/1502179255