In mathematics, spaces of non-positive curvature occur in many contexts and form a generalization of hyperbolic geometry. In the category of Riemannian...

curved space is hyperbolic geometry (see also: non-positive curvature). A space or space-time with zero curvature is called flat. For example, Euclidean space...

{CAT} (k)} neighbourhood. A space with curvature ≤ 0 {\displaystyle \leq 0} may be said to have non-positive curvature. Any CAT ⁡ ( k ) {\displaystyle \operatorname...

geometry, the sectional curvature is one of the ways to describe the curvature of Riemannian manifolds. The sectional curvature K(σp) depends on a two-dimensional...

X {\displaystyle X} be a simply-connected manifold of non-positive bounded sectional curvature. There exist constants C , ε > 0 {\displaystyle C,\varepsilon...

concerning the structure of complete Riemannian manifolds of non-positive sectional curvature. The theorem states that the universal cover of such a manifold...

Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, κ1 and κ2...

there is positive curvature. If Ω < 1, there is negative curvature. Scientists could experimentally calculate Ω to determine the curvature two ways....

In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian...

Bridson, Martin R.; Haefliger, André (1999). Metric spaces of non-positive curvature. Grundlehren der mathematischen Wissenschaften. Vol. 319. Berlin:...