We prove that compact complex manifolds with admitting metrics with negative Chern curvature operator either admit a ddc-exact positive (1, 1) current, or are Kähler with ample canonical bundle. In the case of complex surfaces we obtain a complete classification. The proofs rely on a global existence and convergence result for the pluriclosed flow.
|Original language||English (US)|
|State||Published - Mar 29 2019|
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