Closed, negatively curved Riemannian manifolds with a flat horosphere are hyperbolic

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.

arXiv commentThe authors withdraw this paper because of an error in lemma 3.10