论文标题
多腔恒星拆分赫尔米利亚指标
Pluriclosed Star Split Hermitian Metrics
论文作者
论文摘要
我们介绍了一类Hermitian指标，我们称之为多腔星分裂，概括了Jost和Yau的Astheno-Kähler指标，以及$（N-2）$ - fu-wang-wu的Gauduchon指标。他们通过与任何遗产指标相关的平滑函数的属性与Gauduchon和平衡指标有链接。在指出了几个示例之后，我们将属性推广到一对遗传学指标，并将其概括为由两个复杂的歧管和两个遗传学指标之间的全态图组成的三元组，其中一个是这些歧管。应用程序包括对Fino-Vezzoni猜想的攻击，预测任何承认SKT和平衡指标的紧凑型复杂流形必须是Kähler，我们在额外的假设下肯定地回答。我们还介绍并研究了一个像拉普拉斯一样的差分运算符，订单的两个作用于光滑的$（1，\，1）$ - 遗传歧管的形式。我们证明它是椭圆形的，我们指出了它与纸张第一部分中定义的多颗星分裂指标和对的链接。
We introduce a class of Hermitian metrics, that we call pluriclosed star split, generalising both the astheno-Kähler metrics of Jost and Yau and the $(n-2)$-Gauduchon metrics of Fu-Wang-Wu on complex manifolds. They have links with Gauduchon and balanced metrics through the properties of a smooth function associated with any Hermitian metric. After pointing out several examples, we generalise the property to pairs of Hermitian metrics and to triples consisting of a holomorphic map between two complex manifolds and two Hermitian metrics, one on each of these manifolds. Applications include an attack on the Fino-Vezzoni conjecture predicting that any compact complex manifold admitting both SKT and balanced metrics must be Kähler, that we answer affirmatively under extra assumptions. We also introduce and study a Laplace-like differential operator of order two acting on the smooth $(1,\,1)$-forms of a Hermitian manifold. We prove it to be elliptic and we point out its links with the pluriclosed star split metrics and pairs defined in the first part of the paper.
