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Holomorphic Bisectional Curvature on Total Spaces of Holomorphic Vector Bundles
Abstract
We study complete Kähler metrics with prescribed signs of holomorphic bisectional curvature on total spaces of holomorphic vector bundles over compact complex manifolds. We establish necessary and sufficient conditions in the nonnegative and strictly negative cases, characterized respectively by unitary flatness and Griffiths negativity of the bundle, together with the corresponding curvature conditions on the base. We also obtain a global metric splitting in the nonnegative case, rule out strictly positive curvature over positive-dimensional bases, and construct counterexamples to the converse in the nonpositive case.
Related
- Hermitian manifolds with constant holomorphic sectional curvature or real bisectional curvature
- Non-strict negativity of holomorphic bisectional curvature for compact relative Kähler fibrations
- Global L2 Approximation in the Bergman Spaces with Values in Holomorphic Vector Bundles
- Holomorphic sectional curvature and the Calabi operator on Kähler C-spaces
- A Thullen-type Extension Theorem for Nakano Semi-Positive Holomorphic Vector Bundles
BibTeX
@misc{wang2026holomorphic,
title = {{Holomorphic Bisectional Curvature on Total Spaces of Holomorphic Vector Bundles}},
author = {Xingluan Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15271},
eprint = {2610.15271},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15271},
}
RIS
TY - UNPB
TI - Holomorphic Bisectional Curvature on Total Spaces of Holomorphic Vector Bundles
AU - Xingluan Wang
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15271
UR - https://arxiv.org/abs/2610.15271
AB - We study complete Kähler metrics with prescribed signs of holomorphic bisectional curvature on total spaces of holomorphic vector bundles over compact complex manifolds. We establish necessary and sufficient conditions in the nonnegative and strictly negative cases, characterized respectively by unitary flatness and Griffiths negativity of the bundle, together with the corresponding curvature conditions on the base. We also obtain a global metric splitting in the nonnegative case, rule out strictly positive curvature over positive-dimensional bases, and construct counterexamples to the converse in the nonpositive case.
ER -