论文标题
在Hermitian歧管上，曲率消失
On Hermitian manifolds with vanishing curvature
论文作者
论文摘要
我们表明，在紧凑的复杂歧管上，具有伪芬式的规范束在紧凑的复杂歧管上消失的遗传学指标是完善的。在紧凑的kähler歧管上具有消失的全体形态曲率的多形指标显示为kähler，因此被完全分类。我们证明，在富吉基C类中复杂的歧管上消失的真实双向曲率消失的度量标准是Kähler，因此属于相同的分类。最后，我们正式化了“改变”曲线的概念，该曲线迫使公制结构与其“标准”对应物相吻合时进行区分。
We show that Hermitian metrics with vanishing holomorphic curvature on compact complex manifolds with pseudoeffective canonical bundle are conformally balanced. Pluriclosed metrics with vanishing holomorphic curvature on compact Kähler manifolds are shown to be Kähler and hence, are completely classified. We prove that Hermitian metrics with vanishing real bisectional curvature on complex manifolds in the Fujiki class C are Kähler and thus fall under the same classification. Finally, we formalize the notion of `altered' curvatures, which force distinguished metric structures when mandated to coincide with their `standard' counterparts.
