arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2302.00643math.GRmath.DG
收藏

对称空间$SL(n,\mathbb{R})/SO(n,\mathbb{R})$中Selberg平分面的几何

Geometry of Selberg's bisectors in the symmetric space $SL(n,\mathbb{R})/SO(n,\mathbb{R})$

Department of Mathematics, University of Georgia（佐治亚大学数学系）

Yukun Du

备注：
The most recent revision introduced Lancaster and Rodman's congruence normal form of symmetric matrix pencils and used it to improve the main theorems in Sections 3 and 4. I also added a brief discussion of the isometry equivalent classes of $2$-subspaces of $\mathcal{P}(3)$ to the appendix. Comments are welcome
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

该研究将对称空间$SL(n,\mathbb{R})/SO(n,\mathbb{R})$的黎曼度量替换为Selberg准度量，探讨其相关性质，推广了双曲空间中庞加莱基本多面体定理的对应性质。

摘要：

我们讨论了一类对称空间即$\mathcal{P}(n):=SL(n,\mathbb{R})/SO(n,\mathbb{R})$的若干性质，我们将$\mathcal{P}(n)$上的黎曼度量替换为Selberg提出的准度量。这些性质是双曲空间$\mathbf{H}^n$上与庞加莱基本多面体定理相关性质的推广。

英文摘要：

We study some properties of a family of symmetric spaces, namely $SL(n,\mathbb{R})/SO(n,\mathbb{R})=:\mathcal{P}(n)$, where we replace the Riemannian metric on $\mathcal{P}(n)$ with a premetric suggested by Selberg. These include criteria for intersections of Selberg's bisectors, the shape of Dirichlet-Selberg domains, and angle-like functions between Selberg's bisectors. These properties are generalizations of properties on the hyperbolic spaces $\mathbf{H}^n$ related to Poincaré's fundamental polyhedron theorem.

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。

↑