Introduction

Abstract

In Riemannian geometry, negative curvature usually means negative sectional curvature. Let N be an n-dimensional Riemannian manifold1. 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(·,·).KeywordsModulus SpaceSymmetric SpaceFundamental GroupSectional CurvatureHomotopy ClassThese 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.