# Numerically flat holomorphic bundles over non K\"ahler manifolds

@article{Li2019NumericallyFH, title={Numerically flat holomorphic bundles over non K\"ahler manifolds}, author={Chao Li and Ya Nie and Xi Cheng Zhang}, journal={arXiv: Differential Geometry}, year={2019} }

In this paper, we study numerically flat holomorphic vector bundles over a compact non-K\"ahler manifold $(X, \omega)$ with the Hermitian metric $\omega$ satisfying the Gauduchon and Astheno-K\"ahler conditions. We prove that numerically flatness is equivalent to numerically effectiveness with vanishing first Chern number, semistablity with vanishing first and second Chern numbers, approximate Hermitian flatness and the existence of a filtration whose quotients are Hermitian flat. This gives an…

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A note on pseudo-effective vector bundles with vanishing first Chern number over non-Kähler manifolds

- MathematicsComptes Rendus. Mathématique
- 2021

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