论文标题
涉及$ \ overline \ partial $ -Harmonic $（0,1）$的整体条件 - 表格
An integral condition involving $\overline\partial$-harmonic $(0,1)$-forms
论文作者
论文摘要
我们研究紧凑的几乎复杂的歧管，承认一个偏僻的度量标准，满足了涉及$ \ overline \ partial $ harmonic $（0,1）$ - 表格的整体条件。我们证明，如果紧凑的几乎复杂的歧管上的Hermitian指标非常强烈，则可以自动满足这种整体条件。在进一步的假设是几乎复杂的结构是可以集成的，我们表明高杜琴度量的整体条件等效于强烈的gauduchon。特别是，具有满足整体条件的高杜孔度量的紧凑型复合物表面自动是kähler。如果我们放弃对复杂结构的集成性假设，我们表明存在一个紧凑的几乎复杂的$ 4 $二维的歧管，带有满足整体条件的Hermitian度量，但不承认任何兼容的几乎是Kähler指标。
We study compact almost complex manifolds admitting a Hermitian metric satisfying an integral condition involving $\overline \partial$-harmonic $(0,1)$-forms. We prove that this integral condition is automatically satisfied, if the Hermitian metric on the compact almost complex manifold is strongly Gauduchon. Under the further assumption that the almost complex structure is integrable, we show that the integral condition for a Gauduchon metric is equivalent to be strongly Gauduchon. In particular, a compact complex surface with a Gauduchon metric satisfying the integral condition is automatically Kähler. If we drop the integrability assumption on the complex structure, we show that there exists a compact almost complex $4$-dimensional manifold with a Hermitian metric satisfying the integral condition, but which does not admit any compatible almost-Kähler metric.
