Remarks on Bott residue formula and Futaki–Morita integral invariants
Remarks on Bott residue formula and Futaki–Morita integral invariants
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DOI：
10.1016/j.topol.2012.12.007
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发表时间：
2013-02
影响因子：
0.6
通讯作者：
Ping Li
中科院分区：
文献类型：
--
作者：
Ping Li
当紧致复流形上存在一个非退化的全纯向量场时，著名的Bott留数公式将Chern数的计算归结为该向量场的零集。Futaki不变量阻碍了具有正数量曲率的Kähler-Einstein度量的存在。受Bott留数公式证明的启发，Futaki和Morita定义了一类积分不变量，并给出了与Bott留数公式具有相同特征的相应留数公式，其中包括Futaki原不变量的特例。他们还证明了这些积分不变量的一些性质时，基本流形是凯勒。我们注意到，Futaki和Morita关于这些积分不变量的一些考虑与作者的一些早期文献和最近的工作密切相关。本文的目的是推广它们的一些考虑，并给出这些积分不变量的一些新性质。本说明还讨论了一些相关的评论和文章。
When a compact complex manifold admits a non-degenerate holomorphic vector field, the famous Bott residue formula reduces the calculations of Chern numbers to the zero set of this vector field. The Futaki invariant obstructs the existence of Kähler–Einstein metric with positive scalar curvature. Inspired by the proof of Bott residue formula, Futaki and Morita defined a family of integral invariants, which include Futakiʼs original invariant as a special case, and gave them corresponding residue formulae which have the same feature as that of Bott. They also proved some properties of these integral invariants when the underlying manifolds are Kähler. We remark that some considerations of Futaki and Morita on these integral invariants are closely related to some much earlier literatures and recent work of the author. The purpose of this paper is to generalize some considerations of them and give some new properties of these integral invariants. Some related remarks and articles are also discussed in this note.