arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1107.0617math.DG
收藏

可迁共形和乐群

Transitive conformal holonomy groups

Jesse Alt

备注：
9 pages, LaTeX
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

对于$(M,[g])$，一个签名为$(p,q)$且维数至少为3的共形流形，共形和乐群$\mathrm{Hol}(M,[g]) \subset O(p+1,q+1)$是由$(M,[g])$的正则Cartan几何导出的不变量。我们给出了所有可能的连通共形和乐群的描述，这些共形群传递地作用于莫比乌斯球$S^{p,q}$，签名$(p,q)$的共形结构的齐次模型空间。本说明书的主要部分是列出所有这样的基团，它们也不可约地作用于$\R^{p+1,q+1}$。对于其余的，我们表明，他们必须是紧凑的和分解作用在$\R^{p+1,q+1}$，特别是，由已知的事实共形holonomy的共形类$[g]$必须包含一个度量，这是局部等距的所谓的特殊爱因斯坦产品。

英文摘要：

For $(M,[g])$ a conformal manifold of signature $(p,q)$ and dimension at least three, the conformal holonomy group $\mathrm{Hol}(M,[g]) \subset O(p+1,q+1)$ is an invariant induced by the canonical Cartan geometry of $(M,[g])$. We give a description of all possible connected conformal holonomy groups which act transitively on the Möbius sphere $S^{p,q}$, the homogeneous model space for conformal structures of signature $(p,q)$. The main part of this description is a list of all such groups which also act irreducibly on $\R^{p+1,q+1}$. For the rest, we show that they must be compact and act decomposably on $\R^{p+1,q+1}$, in particular, by known facts about conformal holonomy the conformal class $[g]$ must contain a metric which is locally isometric to a so-called special Einstein product.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑