Some remarks on Hermitian manifolds satisfying Kähler-like conditions
Some remarks on Hermitian manifolds satisfying Kähler-like conditions
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关于满足类凯勒条件的厄米流形的一些评论
DOI：
10.1007/s00209-020-02598-2
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发表时间：
2020
影响因子：
0.8
通讯作者：
Nicoletta Tardini
中科院分区：
文献类型：
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作者：
A. Fino;Nicoletta Tardini
我们研究了Bismut联络满足关于SKT条件和Bimut联络的挠率平行度的第一Bianci恒等式的Hermite度量。我们得到了复曲面具有Hermite度量且其Bismut连接满足第一Bianci恒等式的特征刻画，以及关于Vaisman度量的条件。这些条件，也称为类Bismut Kähler，最近在Angella等人中进行了研究。(Commun anal Geom，将于2018年出现)，Yau等人。(2019)和赵和郑(2019)。利用Arroyo和Lafuente中SKT几乎阿贝尔李群的刻画(Proc Lond Math Soc(3)119：266-289,2019)，我们构造了满足Bismut Kähler条件的Hermite流形的新例子。此外，我们还证明了与复杂曲面上的多闭流和几乎阿贝尔李群上的多闭流有关的一些结果。特别地，我们证明了，如果初始度量具有常的标量曲率，则多闭流在复杂曲面上保持Vaisman条件。
We study Hermitian metrics whose Bismut connectionsatisfies the first Bianchi identity in relation to the SKT condition and the parallelism of the torsion of the Bimut connection. We obtain a characterization of complex surfaces admitting Hermitian metrics whose Bismut connection satisfy the first Bianchi identity and the condition, for every tangent vectorsx,y,z,w, in terms of Vaisman metrics. These conditions, also called Bismut Kähler-like, have been recently studied in Angella et al. (Commun Anal Geom, to appear, 2018), Yau et al. (2019) and Zhao and Zheng (2019). Using the characterization of SKT almost abelian Lie groups in Arroyo and Lafuente (Proc Lond Math Soc (3) 119:266–289, 2019), we construct new examples of Hermitian manifolds satisfying the Bismut Kähler-like condition. Moreover, we prove some results in relation to the pluriclosed flow on complex surfaces and on almost abelian Lie groups. In particular, we show that, if the initial metric has constant scalar curvature, then the pluriclosed flow preserves the Vaisman condition on complex surfaces.