The curvature estimation of the complete Kähler-Einstein metrics on the disk bundles
Abstract
In this paper, we study some geometric properties of the disk bundles over the complete Kähler manifolds. When the base space is the complete Kähler-Einstein manifold, we compute the holomorphic sectional curvature, Riemannian sectional curvature of the complete Kähler-Einstein metric on the disk bundle. Moreover, we present a parametric criteria for whether the manifold admits negative pinched property. When the base space is a bounded pseudoconvex domain equipped with its complete Kähler metric, the corresponding ball bundle in the k-direct sum of line bundles is a bounded pseudoconvex Hartogs domain with fiber dimension k . If the base domain is simply-connected and k≥2, we prove that the Bergman metric on such a Hartogs domain is Kähler-Einstein if and only if the domain is biholomorphically equivalent to a unit ball.
Related
- Kähler-Einstein cone metrics and parabolic bundles
- A complete classification of left-invariant Einstein metrics on S3× S3
- Nonexistence of complete metrics with uniformly positive scalar curvature
- Complete conformal metrics of constant positive scalar curvature with prescribed isolated singularities
- Ample vector bundles without Griffiths-semipositive metrics
BibTeX
@misc{hao2026curvature,
title = {{The curvature estimation of the complete Kähler-Einstein metrics on the disk bundles}},
author = {Yihong Hao and Mingming Chen and An Wang and Ben Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14482},
eprint = {2609.14482},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14482},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The curvature estimation of the complete Kähler-Einstein metrics on the disk bundles
AU - Yihong Hao
AU - Mingming Chen
AU - An Wang
AU - Ben Zhang
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.14482
UR - https://arxiv.org/abs/2609.14482
AB - In this paper, we study some geometric properties of the disk bundles over the complete Kähler manifolds. When the base space is the complete Kähler-Einstein manifold, we compute the holomorphic sectional curvature, Riemannian sectional curvature of the complete Kähler-Einstein metric on the disk bundle. Moreover, we present a parametric criteria for whether the manifold admits negative pinched property. When the base space is a bounded pseudoconvex domain equipped with its complete Kähler metric, the corresponding ball bundle in the k-direct sum of line bundles is a bounded pseudoconvex Hartogs domain with fiber dimension k . If the base domain is simply-connected and k≥2, we prove that the Bergman metric on such a Hartogs domain is Kähler-Einstein if and only if the domain is biholomorphically equivalent to a unit ball.
ER -