On the negatively pinched properties of the disc bundles over negatively pinched Kähler manifolds

2025/09/04 by Hao, Yihong, Chen, Mingming, Wang, An
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.04179

Abstract

In this paper, we study the relation between the existence of a negatively (holomorphically) pinched Kähler metric on a complex manifold M and its disc bundle contained in a Hermitian line bundle over M.

Citations

• Complete complex Finsler metrics and uniform equivalence of the Kobayashi metric
• Invariant metrics on negatively pinched complete Kähler manifolds
• Complex product manifolds cannot be negatively curved
• Negative sectional curvature and the product complex structure

Related

• Kähler manifolds with an almost 1/4-pinched metric
• Non-existence of complete Kähler metric of negatively pinched holomorphic sectional curvature
• Complex product manifolds cannot be negatively curved
• Invariant metrics on negatively pinched complete Kähler manifolds
• Negatively curved Kähler metrics on total spaces of a class of vector bundles