论文标题
复杂（NIL）歧管上的非Kähler结构之间的兼容性
Compatibility between non-Kähler structures on complex (nil)manifolds
论文作者
论文摘要
We study the interplay between the following types of special non-Kähler Hermitian metrics on compact complex manifolds: it locally conformally Kähler, $k$-Gauduchon, balanced and locally conformally balanced and prove that a locally conformally Kähler compact nilmanifold carrying a balanced or a $k$-Gauduchon metric is necessarily a torus.结合2016年Fino和Vezzoni的结果，这导致了这样一个事实，即紧凑的复杂的2步尼尔曼福尔德（Nilmanifold）赋予了以下两种指标：平衡，pluricliclated and pluricliclated and局部综合性的Kähler是圆环。此外，我们在任何具有平衡和局部平衡度量的维度上构建了一个紧凑型尼尔曼福尔德家族，最后我们显示了一个紧凑的复杂尼尔曼福德（Nilmanifold）并不支持左侧不变的本地局部保质性Hyperkähler结构。
We study the interplay between the following types of special non-Kähler Hermitian metrics on compact complex manifolds: it locally conformally Kähler, $k$-Gauduchon, balanced and locally conformally balanced and prove that a locally conformally Kähler compact nilmanifold carrying a balanced or a $k$-Gauduchon metric is necessarily a torus. Combined with a result of Fino and Vezzoni from 2016, this leads to the fact that a compact complex 2-step nilmanifold endowed with whichever two of the following types of metrics: balanced, pluriclosed and locally conformally Kähler is a torus. Moreover, we construct a family of compact nilmanifolds in any dimension carrying both balanced and locally conformally balanced metrics and finally we show a compact complex nilmanifold does not support a left-invariant locally conformally hyperKähler structure.
