Kahler-Einstein Metrics and Integral Invariants
Kahler-Einstein Metrics and Integral Invariants
复制标题
DOI：
10.1007/bfb0078084
复制
发表时间：
1988-06
期刊：
影响因子：
--
通讯作者：
A. Futaki
中科院分区：
文献类型：
--
作者：
A. Futaki
这些注记给出了关于具有正标量曲率的紧致Kähler-Einstein流形的最新结果。这里，由所有全纯向量场组成的复李代数的李代数特征扮演了中心角色，它可以内在地定义在任何紧复流形上，并成为存在Kähler-Einstein度规的障碍。本文收集了有关这一特征标的最新结果，讨论了它的起源、推广、Kähler-Einstein度规存在的充分性以及提升到群特征标。对Calabi等人研究的极值Kähler度量以及Tian和Yau的存在性结果等相关问题也进行了综述。由于详细介绍了凯勒几何和谢恩-西蒙斯理论的基础知识，这些笔记既可供研究生阅读，也可供该学科的专家阅读。
These notes present very recent results on compact Kähler-Einstein manifolds of positive scalar curvature. A central role is played here by a Lie algebra character of the complex Lie algebra consisting of all holomorphic vector fields, which can be intrinsically defined on any compact complex manifold and becomes an obstruction to the existence of a Kähler-Einstein metric. Recent results concerning this character are collected here, dealing with its origin, generalizations, sufficiency for the existence of a Kähler-Einstein metric and lifting to a group character. Other related topics such as extremal Kähler metrics studied by Calabi and others and the existence results of Tian and Yau are also reviewed. As the rudiments of Kählerian geometry and Chern-Simons theory are presented in full detail, these notes are accessible to graduate students as well as to specialists of the subject.