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Rigidity of flat holonomies
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems , First View
- Published online by Cambridge University Press:
- 18 September 2024, pp. 1-30
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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.
