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Numerically flat holomorphic bundles over non-Kähler manifolds

Chao Li , Yanci Nie and Xi Zhang ORCID logo EMAIL logo


In this paper, we study numerically flat holomorphic vector bundles over a compact non-Kähler manifold X which admits an Astheno–Kähler metric. We prove that numerically flatness is equivalent to approximate Hermitian flatness and the existence of a filtration by sub-bundles whose quotients are Hermitian flat. This gives an affirmative answer to the question proposed by Demailly, Peternell and Schneider.

Award Identifier / Grant number: 12141104

Award Identifier / Grant number: 11721101

Award Identifier / Grant number: 11625106

Award Identifier / Grant number: 12001548

Award Identifier / Grant number: 11571332

Funding statement: The research was supported by the National Key R and D Program of China 2020YFA0713100. All authors were supported in part by NSF in China, No. 12141104, 11721101, 11625106, 12001548 and 11571332. The first proof of this paper was completed when the first author and the third author were at School of Mathematical Sciences, University of Science and Technology of China, and the second author was at School of Mathematical Sciences, Xiamen University.


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Received: 2021-10-12
Revised: 2022-06-13
Published Online: 2022-08-10
Published in Print: 2022-09-01

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