Negative holomorphic bisectional curvature of some bounded domains

2024/07/14 by Omar Bakkacha, Bakkacha, Omar
Mathematics · #32Q05 #32Q15 #32T15 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2407.10295

openalex publication_date 2024/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a bounded domain in ℂⁿ admitting a complete Kähler metric with negatively pinched holomorphic bisectional curvature near the boundary, admits a complete Kähler metric with negatively pinched holomorphic bisectional curvature everywhere. As a consequence we prove that strictly pseudoconvex bounded domains with C² boundary and bounded domains with squeezing function tending to 1 at every point of the boundary, admit a complete Kähler metric with negatively pinched holomorphic bisectional curvature everywhere.

Related

• The geometry of domains with negatively pinched Kähler metrics
• Non-existence of complete Kähler metric of negatively pinched holomorphic sectional curvature
• Negatively curved Kähler metrics on total spaces of a class of vector bundles
• Complex product manifolds cannot be negatively curved
• Complete Kähler manifolds with pinched bisectional curvature