Orbifolds and Manifold Quotients with Upper Curvature Bounds

IF 0.4 3区数学 Q4 MATHEMATICS Transformation Groups Pub Date : 2024-01-30 DOI:10.1007/s00031-024-09841-8

引用次数: 0

Abstract

We characterize Riemannian orbifolds with an upper curvature bound in the Alexandrov sense as reflectofolds, i.e., Riemannian orbifolds all of whose local groups are generated by reflections, with the same upper bound on the sectional curvature. Combined with a result by Lytchak–Thorbergsson this implies that a quotient of a Riemannian manifold by a closed group of isometries has locally bounded curvature (from above) in the Alexandrov sense if and only if it is a reflectofold.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

具有上曲率约束的轨道和曲率二次元

摘要我们将具有亚历山德罗夫意义上的曲率上限的黎曼轨道表征为反射表，即其局部群均由反射生成的黎曼轨道表具有相同的截面曲率上限。结合 Lytchak-Thorbergsson 的一个结果，这意味着如果且只有当一个黎曼流形是一个反射流形时，由一个封闭的等向群构成的黎曼流形的商才具有亚历山大罗夫意义上的局部有界曲率（从上而下）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊

Transformation Groups 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

100

审稿时长

9 months

期刊介绍： Transformation Groups will only accept research articles containing new results, complete Proofs, and an abstract. Topics include: Lie groups and Lie algebras; Lie transformation groups and holomorphic transformation groups; Algebraic groups; Invariant theory; Geometry and topology of homogeneous spaces; Discrete subgroups of Lie groups; Quantum groups and enveloping algebras; Group aspects of conformal field theory; Kac-Moody groups and algebras; Lie supergroups and superalgebras.

期刊最新文献

A Remark on Torsors under Affine Group Schemes. Stability of $$\imath $$ canonical Bases of Locally Finite Type Counting Parabolic Principal G-Bundles with Nilpotent Sections Over $$\mathbb {P}^{1}$$ Regularity of Unipotent Elements in Total Positivity Rational Singularities for Moment Maps of Totally Negative Quivers