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 xN, defined by the Riemannian metric will be denoted by (·,·), the Levi-Civita connection by ∇, and its curvature tensor by R(·,·).


Modulus Space Symmetric Space Fundamental Group Sectional Curvature Homotopy Class 
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Copyright information

© Springer Basel AG 1997

Authors and Affiliations

  • Jürgen Jost
    • 1
  1. 1.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany

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