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Kähler Rigidity for Constant Chern Holomorphic Sectional Curvature
We prove two rigidity theorems for compact Hermitian manifolds with constant Chern holomorphic sectional curvature. On a manifold in Fujiki's class $\mathcal C$, every Hermitian metric of constant nonpositive Chern holomorphic sectional curvature is Kähler, without a balanced or pluriclosed assumpti
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