Approximation and extension of Hermitian metrics on holomorphic vector bundles over Stein manifolds
Year: 2024
Type: article
Abstract: We show that a singular Hermitian metric on a holomorphic vector bundle over a Stein manifold which is negative in the sense of Griffiths (resp. Nakano) can be approximated by a sequence of smooth Hermitian metrics with the same curvature negativity. We also show that a smooth Hermitian metric on a holomorphic vector bundle over a Stein manifold restricted to a submanifold which is negative in the sense of Griffiths (resp. Nakano) can be extended to the whole bundle with the same curvature negativity.
Source: Comptes Rendus Mathématique
DOI: 10.5802/crmath.675
Authors: Fusheng Deng, Jiafu Ning, Zhiwei Wang, Xiangyu Zhou
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404693226