Chern Holomorphic Sectional Curvature: Canonical Ampleness, Rigidity, and Flatness Counterexamples

Xiangsen Qin, Yuanhong Tian

Let $X$ be a compact Brody-hyperbolic complex manifold admitting a strictly positive real $(1,1)$-current $T$ with smooth $dT$ and $d{d}^{c}T\le 0$. We prove that the canonical bundle $…