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 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.
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