Geometry of Calabi-Yau Metrics
Geometry of Calabi-Yau Metrics
复制标题
卡拉比-丘度量的几何
DOI：
10.1090/noti2454
复制
发表时间：
2022
影响因子：
--
通讯作者：
Sun, Song
中科院分区：
文献类型：
--
作者：
Sun, Song
Calabi-Yau度规的一个显著特征是它们具有消失的里奇曲率，因此提供了黎曼真空爱因斯坦方程的解。这可以由安布罗斯-辛格完整定理和比安奇恒等式推导出来。在黎曼完整群的Berger分类中，Calabi-Yau度量是具有特殊完整的黎曼度量的一个例子，在弦理论中起着关键的作用。这篇文章是作者最近的一些讨论会和小型学校讲座笔记的扩充版。这里的主要目标是向读者解释卡拉比-丘度量的一些结构和几何；同时，我们将有选择地讨论该领域的几个有趣的例子和一些最近的研究进展。显然，本文绝不是对这一主题的全面历史考察。主题只是根据作者的个人品味选择的，还有许多其他相关的论文强调不同的方面。此外，由于篇幅有限，不可能提供以下所有结果的精确参考，但作者希望感兴趣的读者可以轻松地自行查找进一步的细节。
A salient feature of Calabi-Yau metrics is that they have vanishing Ricci curvature, hence provide solutions to the Riemannian vacuum Einstein equation. This can be deduced as a consequence of the Ambrose-Singer holonomy theorem and the Bianchi identity. In terms of the Berger classification of Riemannian holonomy groups, Calabi-Yau metrics are examples of Riemannian metrics with special holonomy, which play a pivotal role in string theory.This article is an expanded version of the notes for some recent colloquia and mini-school lectures given by the author. The main goal here is to explain to the readers some constructions and the geometry of Calabi-Yau metrics; in the meantime we aim to selectively discuss several interesting examples in the field and some recent research progress. Obviously, this article is by no means supposed to be a comprehensive historic survey of the subject. The topics are merely chosen according to the personal taste of the author, and there are many other related papers emphasizing different aspects. Also, for lack of space it is impossible to provide precise references to all the results mentioned below, but the author hopes that interested readers can easily look up further details on their own.
Calabi-Yau 度量的复杂结构退化和崩溃
DOI：
10.1090/s0894-0347-1990-1040196-6
发表时间：
2019
期刊：
arXiv: Differential Geometry
影响因子：
--
作者：
Song Sun;Ruobing Zhang
通讯作者：
Ruobing Zhang
DOI：
10.1090/pspum/052.2
发表时间：
1991
期刊：
--
影响因子：
--
作者：
Eric Bedford;J. D'Angelo;R. Greene;S. Krantz
通讯作者：
Eric Bedford;J. D'Angelo;R. Greene;S. Krantz
胶合卡拉比 - 节点 3 倍的 Yau 度量
DOI：
--
发表时间：
2022
期刊：
影响因子：
--
作者：
Cho Joseph;Leschke Katrin;Ogata Yuta;Ogata Yuta;緒方 勇太;Yanagishita Masahiro;柳下 剛広;Yohsuke Imagi;Y Imagi;Yohsuke Imagi;Yohsuke Imagi
通讯作者：
Yohsuke Imagi