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

共 50 条

[1] Commuting holonomies and rigidity of holomorphic foliations
Movasati, Hossein
Nakai, Isao
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2008, 40 : 473 - 478
[2] Flat holonomies on automata networks
Itkis, G
Levin, LA
STACS 2006, PROCEEDINGS, 2006, 3884 : 23 - 49
[3] Flat equivariant gerbes: holonomies and dualities
Cheng, Peng
Melnikov, Ilarion V.
Minasian, Ruben
JOURNAL OF HIGH ENERGY PHYSICS, 2023, 2023 (04)
[4] Flat equivariant gerbes: holonomies and dualities
Peng Cheng
Ilarion V. Melnikov
Ruben Minasian
Journal of High Energy Physics, 2023
[5] Flat connections with non-diagonalizable holonomies
Selivanov, K
PHYSICS LETTERS B, 1999, 471 (2-3) : 171 - 173
[6] Flat metrics, cubic differentials and limits of projective holonomies
Loftin, John
GEOMETRIAE DEDICATA, 2007, 128 (01) : 97 - 106
[7] Flat metrics, cubic differentials and limits of projective holonomies
John Loftin
Geometriae Dedicata, 2007, 128 : 97 - 106
[8] An improved cosmic crystallography method to detect holonomies in flat spaces
Fujii, H.
Yoshii, Y.
ASTRONOMY & ASTROPHYSICS, 2011, 529
[9] Focal rigidity of flat tori
Kwakkel, Ferry
Martens, Marco
Peixoto, Mauricio
ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS, 2011, 83 (04): : 1149 - 1158
[10] HOMOTOPY MINIMAL PERIOD SELF-MAPS ON FLAT MANIFOLDS WITH CYCLIC HOLONOMIES
Liang, Zhibin
Zhao, Xuezhi
ASIAN JOURNAL OF MATHEMATICS, 2013, 17 (04) : 645 - 651

← 1 2 3 4 5 →