2019/01/15 by Li, Chao, Nie, Yanci, Zhang, Xi · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1901.04680
In this paper, we study numerically flat holomorphic vector bundles over a compact non-Kähler manifold (X, ω) with the Hermitian metric ω satisfying the Gauduchon and Astheno-Kähler 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.