Rigidity of flat holonomies - Archive ouverte HAL
Article Dans Une Revue Ergodic Theory and Dynamical Systems Année : 2024

Rigidity of flat holonomies

Résumé

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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Dates et versions

hal-04735210 , version 1 (14-10-2024)

Identifiants

Citer

Gérard Besson, Gilles Courtois, Sa’ar Hersonsky. Rigidity of flat holonomies. Ergodic Theory and Dynamical Systems, 2024, Ergodic Theory and Dynamical Systems, pp.1-30. ⟨10.1017/etds.2024.58⟩. ⟨hal-04735210⟩
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