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 Space Symmetric Space Fundamental Group Sectional Curvature Homotopy Class
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