Rigidity of flat holonomies

Abstract

We prove that the existence of one horosphere in the universal cover of a closed, strictly quarter pinched, negatively curved Riemannian manifold of dimension $n\ge 3$ on which the stable holonomy along minimizing geodesics coincide with the Riemannian parallel transport, implies that the manifold is homothetic to a real hyperbolic manifold.

arXiv admin note: substantial text overlap with arXiv:1701.06883