平面整体的刚性

IF 0.8 3区 数学 Q2 MATHEMATICS
GÉRARD BESSON, GILLES COURTOIS, SA’AR HERSONSKY
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引用次数: 0

摘要

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。
Rigidity of flat holonomies
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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来源期刊
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.
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