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arXiv · 2309.04964

Approximation and extension of Hermitian metrics on holomorphic vector bundles over Stein manifolds

Fusheng Deng·Jiafu Ning·Zhiwei Wang·Xiangyu Zhou
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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.

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Fusheng Deng, Jiafu Ning, Zhiwei Wang, Xiangyu Zhou. 2023-09-10. Approximation and extension of Hermitian metrics on holomorphic vector bundles over Stein manifolds. https://arxiv.org/abs/2309.04964

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