Rigidity of flat holonomies

IF 0.8 3区数学 Q2 MATHEMATICS

Ergodic Theory and Dynamical Systems Pub Date : 2024-09-18 DOI:10.1017/etds.2024.58

GÉRARD BESSON, GILLES COURTOIS, SA’AR HERSONSKY

引用次数: 0

Abstract

We prove that the existence of one horosphere in the universal cover of a closed Riemannian manifold of dimension

$n \geq 3$

with strongly

$1/4$

-pinched or relatively

$1/2$

-pinched sectional curvature, on which the stable holonomy along one horosphere coincides with the Riemannian parallel transport, implies that the manifold is homothetic to a real hyperbolic manifold.

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平面整体的刚性

我们证明，在维数为 $n \geq 3$、截面曲率为强 1/4$ -夹角或相对 1/2$ -夹角的封闭黎曼流形的普适盖中存在一个角层，其上沿一个角层的稳定整体性与黎曼平行传输重合，这意味着该流形与实双曲流形同构。

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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来源期刊

Ergodic Theory and Dynamical Systems 数学-数学

CiteScore

1.70

自引率

11.10%

发文量

113

审稿时长

6-12 weeks

期刊介绍： Ergodic Theory and Dynamical Systems focuses on a rich variety of research areas which, although diverse, employ as common themes global dynamical methods. The journal provides a focus for this important and flourishing area of mathematics and brings together many major contributions in the field. The journal acts as a forum for central problems of dynamical systems and of interactions of dynamical systems with areas such as differential geometry, number theory, operator algebras, celestial and statistical mechanics, and biology.