Year: 2026
Type: preprint
Abstract: We study complete K$ä$hler 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.
Source: arXiv (Cornell University)
Author: Wang, Xingluan
Institution: University of Science and Technology of China
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221807811