论文标题
关于Oeljeklaus-Toma歧管的特殊Hermitian指标
Special Hermitian metrics on Oeljeklaus-Toma manifolds
论文作者
论文摘要
Oeljeklaus-Toma（OT）歧管是Inoue-Bombieri表面的较高维度类似物，它们的构造与有限的扩展名$ k $ $ q $和一个子组$ u $相关。我们表征了复数指标的存在（也称为强烈的k \“ ahler具有扭转（SKT）指标），这在数量理论条件上纯粹是纯粹的$ x（k，u）$纯粹在数量理论条件上，对第三个betti number $ b_3 $ and the dolbeault Coohomology unded限制$ h^{2,1} _ {\ edline {\ partial}} $与[D20]的主要结果相结合，这些数值条件在任意复杂的尺寸中呈现了多个元素的$（2，$）$，$（2，$），也就是说，这相当于$ b_3 = 2 $，我们提供了一个携带多数级指标的复杂维度4的ot歧管。
Oeljeklaus-Toma (OT) manifolds are higher dimensional analogues of Inoue-Bombieri surfaces and their construction is associated to a finite extension $K$ of $Q$ and a subgroup of units $U$. We characterize the existence of pluriclosed metrics (also known as strongly K\" ahler with torsion (SKT) metrics) on any OT manifold $X(K, U)$ purely in terms of number-theoretical conditions, yielding restrictions on the third Betti number $b_3$ and the Dolbeault cohomology group $H^{2,1}_{\overline{\partial}}$. Combined with the main result in [D20], these numerical conditions render explicit examples of pluriclosed OT manifolds in arbitrary complex dimension. We prove that in complex dimension 4 and type $(2, 2)$, the existence of a pluriclosed metric on $X(K, U)$ is entirely topological, namely, it is equivalent to $b_3 = 2$. Moreover, we provide an explicit example of an OT manifold of complex dimension 4 carrying a pluriclosed metric. Finally, we show that no OT manifold admits balanced metrics, but all of them carry instead locally conformally balanced metrics.
