论文标题
完全卡勒的不存在负捏性全态分段曲率的度量
Non-existence of complete Kähler metric of negatively pinched holomorphic sectional curvature
论文作者
论文摘要
我们显示的定理为完全kähler的不存在提供了足够的条件 - 负标量曲率的骨曲率曲率的骨膜曲率负面曲率是负面的： 让$ω$在$ \ mathbb {c}^n $中是一个有界的虚弱的pseudoconvex域，带有kähler公制$ω$，其全体形状截面曲率在$ω$的拓扑边界附近为负（相对于$ \ mathbb {c}^n $）的拓扑边界（相对于$ \ n $）和$ $ om $ $ $ $ - 然后，$ω$统一等同于Kobayashi-Royden度量标准，以下二分法保持： 1。$ω$已完成，$ω$均匀地等同于完整的Kähler-ineinstein指标，具有负标态曲率。 2。$ω$不完整，并且没有完整的kähler指标，而骨膜截面截面呈负偏度。此外，$ω$是Carathéodory不完整。 我们的方法是基于构建负面捏合截面曲率的Kähler指标，并应用了受Wu-Yau启发的不变度指标的含义。
We show the theorem which provides some sufficient condition to the non-existence of a complete Kähler--Einstein metric of negative scalar curvature whose holomorphic sectional curvature is negatively pinched: Let $Ω$ be a bounded weakly pseudoconvex domain in $\mathbb{C}^n$ with a Kähler metric $ω$ whose holomorphic sectional curvature is negative near the topological boundary of $Ω$ (with respect to relative topology of $\mathbb{C}^n$) and $ω$ admits the quasi-bounded geometry. Then $ω$ is uniformly equivalent to the Kobayashi--Royden metric and the following dichotomy holds: 1. $ω$ is complete, and $ω$ is uniformly equivalent to the complete Kähler--Einstein metric with negative scalar curvature. 2. $ω$ is incomplete, and there is no complete Kähler metric with negatively pinched holomorphic sectional curvature. Moreover, $Ω$ is Carathéodory incomplete. Our approach is based on the construction of a Kähler metric of negatively pinched holomorphic sectional curvature and applying the implication of equivalence of invariant metrics inspired by Wu-Yau.
