English

Rigidity of flat holonomies

Differential Geometry 2024-07-30 v2 Dynamical Systems

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 n3n\geq 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.

Keywords

Cite

@article{arxiv.2308.14136,
  title  = {Rigidity of flat holonomies},
  author = {Gérard Besson and Gilles Courtois and Sa'ar Hersonsky},
  journal= {arXiv preprint arXiv:2308.14136},
  year   = {2024}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1701.06883

R2 v1 2026-06-28T12:05:27.169Z