论文标题
Dinew-Popovici Energy功能的临界点的特性
Properties of Critical Points of the Dinew-Popovici Energy Functional
论文作者
论文摘要
最近，Dinew和Popovici介绍并研究了一个能量功能$ F $，该$ F $ f $ fos of Hermitian-symplectic Metric的AEPPLI同胞类别中的指标，并表明在维度3中，其关键点（如果有）是Kähler。在本文中，我们进一步研究了该功能在较高维度和尸体变形下的关键点。我们首先证明，对于$ f $而言，这是一个关闭的关键点，这是全体形态变形下的封闭财产。然后，我们证明AEPPLI同胞类中的KählerMetric$ω_k$的存在是在Holomorphic变形下的开放属性。此外，我们考虑了$（2，\，0）$ - 扭转形式的$ρ_Ω ^{2，\，0} $的$ρ_Ω最后，当$（2，\，0）$ - 扭转式$ρ_Ω ^{2，\，0} $是$ \ partial $ -exact时，我们给出了$ f $差异的明确公式。
Recently, Dinew and Popovici introduced and studied an energy functional $F$ acting on the metrics in the Aeppli cohomology class of a Hermitian-symplectic metric and showed that in dimension 3 its critical points (if any) are Kähler. In this article we further investigate the critical points of this functional in higher dimensions and under holomorphic deformations. We first prove that being a critical point for $F$ is a closed property under holomorphic deformations. We then show that the existence of a Kähler metric $ω_k$ in the Aeppli cohomology class is an open property under holomorphic deformations. Furthermore, we consider the case when the $(2,\,0)$-torsion form $ρ_ω ^{2,\,0}$ of $ω$ is $\partial$-exact and prove that this property is closed under holomorphic deformations. Finally, we give an explicit formula for the differential of $F$ when the $(2,\,0)$-torsion form $ρ_ω ^{2,\,0}$ is $\partial$-exact.
