论文标题
紧凑的复杂歧管产品是否会允许LCK指标？
Do products of compact complex manifolds admit LCK metrics?
论文作者
论文摘要
LCK（当地的kahler）歧管是一个遗传歧管，它接纳了一个卡勒的盖子，其甲板小组与Holomorphic Hymotheties有关Kahler Metric的作用。两个LCK歧管的乘积没有天然产物LCK结构。据推测，两个紧凑的复合歧管的产物永远不会是LCK。我们将所有已知的紧凑型LCK歧管示例分类为三个非独家类：具有潜力的LCK，我们称为inoue类型的一类歧管，以及包含有理曲线的lck。在本文中，我们证明了LCK歧管和属于这三个类之一的LCK歧管的产物不接受LCK结构。
An LCK (locally conformally Kahler) manifold is a Hermitian manifold which admits a Kahler cover with deck group acting by holomorphic homotheties with respect to the Kahler metric. The product of two LCK manifolds does not have a natural product LCK structure. It is conjectured that a product of two compact complex manifolds is never LCK. We classify all known examples of compact LCK manifolds onto three not exclusive classes: LCK with potential, a class of manifolds we call of Inoue type, and those containing a rational curve. In the present paper, we prove that a product of an LCK manifold and an LCK manifold belonging to one of these three classes does not admit an LCK structure.
