关于Poincaré型Kähler度量和Futaki特征标的注记
Note on Poincaré type Kähler metrics and Futaki characters
摘要：
在紧致Kähler流形X中，单正规交叉因子D的补X \D上的Poincaré型Kähler度量是X \D上的Kähler度量，沿D具有尖点奇点。我们与Futaki字符的全纯向量场平行的除数，定义为任何固定的庞加莱型Kähler类，经典的Futaki字符的相对光滑类。作为应用，我们用平均数量曲率和Futaki特征表示了极值Poincaré型Kähler度量存在的数值障碍.
英文摘要：
A Poincaré type Kähler metric on the complement X\D of a simple normal crossing divisor D, in a compact Kähler manifold X, is a Kähler metric on X\D with cusp singularity along D. We relate the Futaki character for holomorphic vector fields parallel to the divisor, defined for any fixed Poincaré type Kähler class, to the classical Futaki character for the relative smooth class. As an application we express a numerical obstruction to the existence of extremal Poincaré type Kähler metrics, in terms of mean scalar curvatures and Futaki characters.
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