About: Non-positive curvature

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In mathematics, spaces of non-positive curvature occur in many contexts and form a generalization of hyperbolic geometry. In the category of Riemannian manifolds, one can consider the sectional curvature of the manifold and require that this curvature be everywhere less than or equal to zero. The notion of curvature extends to the category of geodesic metric spaces, where one can use comparison triangles to quantify the curvature of a space; in this context, non-positively curved spaces are known as (locally) CAT(0) spaces.

Attributes	Values
rdfs:label	Non-positive curvature (en)
rdfs:comment	In mathematics, spaces of non-positive curvature occur in many contexts and form a generalization of hyperbolic geometry. In the category of Riemannian manifolds, one can consider the sectional curvature of the manifold and require that this curvature be everywhere less than or equal to zero. The notion of curvature extends to the category of geodesic metric spaces, where one can use comparison triangles to quantify the curvature of a space; in this context, non-positively curved spaces are known as (locally) CAT(0) spaces. (en)
dcterms:subject	Curvature (mathematics) Hyperbolic geometry Metric geometry
Wikipage page ID	12989803 (xsd:integer)
Wikipage revision ID	913776193 (xsd:integer)
Link from a Wikipage to another Wikipage	Pseudosphere Mostow rigidity theorem CAT(0) space Hyperbolic group Riemann surface Mathematics Genus Geometric group theory Gauss–Bonnet theorem Geometry Graph (discrete mathematics) Curvature (mathematics) Combinatorics Comparison triangle Category (category theory) Topology Hyperbolic geometry Flat torus Riemannian manifold Riemannian metric Hyperbolic geometry Hyperbolic manifold Metric geometry Homeomorphism Manifold Orbifold Margulis lemma Uniformization theorem Euclidean plane Euler characteristic Sectional curvature Hyperbolic metric Hyperbolic plane Geodesic metric space
sameAs	Non-positive curvature Non-positive curvature Non-positive curvature
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Geometry-stub dbt:MathSciNet
has abstract	In mathematics, spaces of non-positive curvature occur in many contexts and form a generalization of hyperbolic geometry. In the category of Riemannian manifolds, one can consider the sectional curvature of the manifold and require that this curvature be everywhere less than or equal to zero. The notion of curvature extends to the category of geodesic metric spaces, where one can use comparison triangles to quantify the curvature of a space; in this context, non-positively curved spaces are known as (locally) CAT(0) spaces. (en)
prov:wasDerivedFrom	wikipedia-en:Non-positive_curvature?oldid=913776193&ns=0
page length (characters) of wiki page	5084 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Non-positive_curvature
is Link from a Wikipage to another Wikipage of	Non-positively curved space Curved space Geodesic bicombing Configuration space (mathematics) CAT(k) space Amenable group F. Thomas Farrell Eilenberg–MacLane space Tutte embedding
is Wikipage redirect of	Non-positively curved space
is foaf:primaryTopic of	wikipedia-en:Non-positive_curvature

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