Closed, negatively curved Riemannian manifolds with a flat horosphere are hyperbolic
Differential Geometry
2017-02-06 v2
Abstract
We prove that the existence of one flat horosphere in the universal cover of a closed, strictly quarter pinched, negatively curved Riemannian manifold of dimension n with n greater than or equal to 3, implies that the manifold is homothetic to a real hyperbolic manifold.
Keywords
Cite
@article{arxiv.1701.06883,
title = {Closed, negatively curved Riemannian manifolds with a flat horosphere are hyperbolic},
author = {Gérard Besson and Gilles Courtois and Sa'ar Hersonsky},
journal= {arXiv preprint arXiv:1701.06883},
year = {2017}
}
Comments
The authors withdraw this paper because of an error in lemma 3.10