论文标题
Dolbeault Harmonic $（1,1）$ - $ 4 $二维紧凑型的谎言组的表格几乎是hermitian结构
Dolbeault Harmonic $(1,1)$-forms on $4$-dimensional compact quotients of Lie Groups with a left invariant almost Hermitian structure
论文作者
论文摘要
我们研究dolbeault谐波$（1,1）$ - 紧凑型商的表格$ m =γ\ backslash g $ $ 4 $二维的躺椅$ g $承认左不变的几乎是Hermitian结构$（j，ω）$。在这种情况下，我们证明了$（m，j，ω）上的dolbeault谐波$（1,1）$的空间$ b^ - +1 $当时，并且仅当存在左左dual dual $ dual $（1,1）$ - $（g，j，g，j）$ in $ iD $ id^cγ= d的$（g，j）$γ$。否则，其尺寸为$ b^ - $。这样，我们回答了张的问题。
We study Dolbeault harmonic $(1,1)$-forms on compact quotients $M=Γ\backslash G$ of $4$-dimensional Lie groups $G$ admitting a left invariant almost Hermitian structure $(J,ω)$. In this case, we prove that the space of Dolbeault harmonic $(1,1)$-forms on $(M,J,ω)$ has dimension $b^-+1$ if and only if there exists a left invariant anti self dual $(1,1)$-form $γ$ on $(G,J)$ satisfying $id^cγ=dω$. Otherwise, its dimension is $b^-$. In this way, we answer to a question by Zhang.
