Compact Kähler manifolds with quasi-positive second Chern-Ricci curvature

Abstract

Let $X$ be a compact Kähler manifold. We prove that if $X$ admits a smooth Hermitian metric $\omega$ with quasi-positive second Chern-Ricci curvature ${\mathrm{Ric}}^{(2)}(\omega )$, then $X$ is projective and rationally connected. In particular, $X$ is simply connected.

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Cited by in corpus (1)

• Deformation of Hermitian metrics