Introduction

In Riemannian geometry, negative curvature usually means negative sectional curvature. Let N be an n-dimensional Riemannian manifold 1 . All Riemannian manifolds will be assumed to be connected and complete unless the contrary is explicitly stated. The scalar product on T x N , for x ∈ N , defined by the Riemannian metric will be denoted by (·,·), the Levi-Civita connection by ∇, and its curvature tensor by R (·,·). These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.