Numerically flat holomorphic bundles over non K\"ahler manifolds
Differential Geometry
2019-02-26 v2
Abstract
In this paper, we study numerically flat holomorphic vector bundles over a compact non-K\"ahler manifold with the Hermitian metric 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 affirmative answer to the question proposed by Demailly, Peternell and Schneider.
Cite
@article{arxiv.1901.04680,
title = {Numerically flat holomorphic bundles over non K\"ahler manifolds},
author = {Chao Li and Yanci Nie and Xi Zhang},
journal= {arXiv preprint arXiv:1901.04680},
year = {2019}
}