摘要
在万学远和王煦的文章中,他们证明了Monge-Ampère纤维化的基流形上广义Weil-Petersson度量的全纯双截曲率的非正性.在此基础上,本文进一步刻画了全纯双截面曲率在等号成立时所需满足的条件;另外,对于具有相对Kähler纤维化的紧复曲面,证明了当其signature为零时Monge-Ampère形式的存在性;最后,在射影丛纤维化的情况下,证明了当且仅当在反典范丛的第一陈类中存在半正定的Kähler形式时,它是一个Monge-Ampère纤维化.
In their paper,Wan and Wang established the non-positivity of the holomorphic bisectional curvature of a generalized Weil-Petersson metric on the base manifold of a MongeAmpère fibration.This paper presents a precise characterization of the vanishing of the holomorphic bisectional curvature.On the other hand,for a compact complex surface admitting a relative Kähler fibration,the author demonstrates the existence of a MongeAmpère form whenever its signature vanishes.Furthermore,in the context of a projective bundle fibration,the author establishes that it is a Monge-Ampère fibration if and only if there exists a semi-positive relative Kähler form in the first Chern class of the relative anti-canonical bundle.
作者
刘洪伶
LIU Hongling(School of Science,Chongqing University of Technology,Chongqing 400054,China)
出处
《数学年刊(A辑)》
北大核心
2025年第3期311-320,共10页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.12101093)的资助。
