Orbifolds and Manifold Quotients with Upper Curvature Bounds

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.

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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。

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