Remark on quasi-negative k-Ricci curvature

2025/08/24 by Zhang, Shiyu · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.17237

Abstract

In this note, we show that if X is a compact Kähler manifold with k-quasi-negative Ricci curvature, then K_X is ample. This completes a previous result of Chu-Lee-Tam. The key ingredient is an observation that any rational curve C on X satisfy K_X⋅ C>0 based on the Gauss-Codazzi equation.

Citations

• Fundamental groups of compact Kähler manifolds with semi-positive holomorphic sectional curvature
• On the structure of compact Kähler manifolds with nonnegative holomorphic sectional curvature
• An application of a C²-estimate for a complex Monge-Ampère equation
• Kähler manifolds and mixed curvature
• On projective manifolds with semi-positive holomorphic sectional curvature
• Liouville theorems and a Schwarz Lemma for holomorphic mappings between Kähler manifolds
• A remark on our paper "Negative Holomorphic curvature and positive canonical bundle"
• Quasi-negative holomorphic sectional curvature and positivity of the\n canonical bundle
• On projective Kähler manifolds of partially positive curvature and rational connectedness

Cited by

• Hermitian manifolds with nonpositive holomorphic sectional curvature

Related

• Non-negative Ricci curvature on closed manifolds under Ricci flow
• Remarks on Kähler Orbifolds of non-negative Ricci curvature
• On almost quasi-negative holomorphic sectional curvature
• Quasi-projective manifolds with negative holomorphic sectional curvature
• Quasi-positive curvature and projectivity