Rigidity of flat holonomies

被引：0

作者：

Besson, Gerard ^{[1
]}

Courtois, Gilles ^{[2
]}

Hersonsky, Sa'ar ^{[3
]}

机构：

[1] Univ Grenoble Alpes, CNRS, Inst Fourier, CS 40700, F-38058 Grenoble 09, France

[2] Sorbonne Univ, CNRS, UMR 7586, Inst Math Jussieu Paris Rive Gauche,Fac Sci, F-75252 Paris 05, France

[3] Univ Georgia, Dept Math, Athens, GA 30602 USA

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2025年 / 45卷 / 04期

基金：

欧洲研究理事会;

关键词：

negatively curved Riemannian manifolds; rigidity; horospheres; holonomy; LYAPUNOV EXPONENTS; COCYCLES;

D O I：

10.1017/etds.2024.58

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1048 / 1077

页数：30

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