论文标题
关于格劳特的完整kähler指标的例子
On Grauert's examples of complete Kähler metrics
论文作者
论文摘要
格劳特（Grauert）表明，完整的kähler指标的存在并不能通过在Holomorphy领域的复杂分析集的补充上构造此类指标来表征Holomorphy的域。在本说明中，我们研究了两个原型情况下此类度量的圆形分段曲率是至少两个的编构象的超平面。这是通过计算其限制到这两个示例中合适的全态叶片叶片的高斯曲率来完成的。我们还在穿刺平面$ \ mathbb {c}^{\ ast} $上检查了此指标，并表明在这种情况下它的行为非常不同。
Grauert showed that the existence of a complete Kähler metric does not characterize domains of holomorphy by constructing such metrics on the complements of complex analytic sets in a domain of holomorphy. In this note, we study the holomorphic sectional curvatures of such metrics in two prototype cases namely, $\mathbb{C}^n \setminus \{0\}, n \ge 2$ and $\mathbb{B}^N \setminus A$, $N \ge 2$ and $A \subset \mathbb{B}^N$ is a hyperplane of codimension at least two. This is done by computing the Gaussian curvature of its restriction to the leaves of a suitable holomorphic foliation of these two examples. We also examine this metric on the punctured plane $\mathbb{C}^{\ast}$ and show that it behaves very differently in this case.
