Rigidity of flat holonomies

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 transpo...

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Veröffentlicht in:Ergodic theory and dynamical systems 2024-09, p.1-30
Hauptverfasser: BESSON, GÉRARD, COURTOIS, GILLES, HERSONSKY, SA’AR
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
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Zusammenfassung: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.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2024.58