Yuan-Hong Tian

Constant Chern Holomorphic Sectional Curvature: Rigidity and Counterexamples to the Flatness Conjecture

We prove rigidity results for Hermitian metrics of constant Chern holomorphic sectional curvature and construct counterexamples to the flatness conjecture. On a compact complex manifold in Fujiki's class $\mathcal C$ of dimension $n\ge2$, every such metric with nonpositive curvature is K\"ahler; its universal cover is...