About: Killing–Hopf theorem

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In geometry, the Killing–Hopf theorem states that complete connected Riemannian manifolds of constant curvature are isometric to a quotient of a sphere, Euclidean space, or hyperbolic space by a group acting freely and properly discontinuously. These manifolds are called space forms. The Killing–Hopf theorem was proved by Killing and Hopf.

Attributes	Values
rdf:type	yago:WikicatTheoremsInRiemannianGeometry yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293
rdfs:label	Killing–Hopf theorem (en) Killing–Hopfs sats (sv)
rdfs:comment	In geometry, the Killing–Hopf theorem states that complete connected Riemannian manifolds of constant curvature are isometric to a quotient of a sphere, Euclidean space, or hyperbolic space by a group acting freely and properly discontinuously. These manifolds are called space forms. The Killing–Hopf theorem was proved by Killing and Hopf. (en) Inom matematiken är Killing–Hopfs sats ett resultat som säger att en fullständig sammanhängande Riemannmångfald av konstant krökning är isometrisk till ett av en sfär, ett Euklidiskt rum eller ett med en grupp som verkar fritt och . Dessa mångfalder är kända som . Killing–Hopfs sats bevisades av Killing och Hopf. (sv)
dcterms:subject	Theorems in Riemannian geometry Riemannian geometry
Wikipage page ID	37711150 (xsd:integer)
Wikipage revision ID	1053923079 (xsd:integer)
Link from a Wikipage to another Wikipage	Theorems in Riemannian geometry Properly discontinuous action Mathematische Annalen Euclidean space Quotient space (topology) Riemannian manifold Group (mathematics) Group action (mathematics) Rigid transformation Hyperbolic space Riemannian geometry Sphere Space form
sameAs	Killing–Hopf theorem Killing–Hopf theorem Killing–Hopf theorem Killing–Hopf theorem
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Geometry-stub dbt:Short_description dbt:Harvs dbt:Manifolds
has abstract	In geometry, the Killing–Hopf theorem states that complete connected Riemannian manifolds of constant curvature are isometric to a quotient of a sphere, Euclidean space, or hyperbolic space by a group acting freely and properly discontinuously. These manifolds are called space forms. The Killing–Hopf theorem was proved by Killing and Hopf. (en) Inom matematiken är Killing–Hopfs sats ett resultat som säger att en fullständig sammanhängande Riemannmångfald av konstant krökning är isometrisk till ett av en sfär, ett Euklidiskt rum eller ett med en grupp som verkar fritt och . Dessa mångfalder är kända som . Killing–Hopfs sats bevisades av Killing och Hopf. (sv)
prov:wasDerivedFrom	wikipedia-en:Killing–Hopf_theorem?oldid=1053923079&ns=0
page length (characters) of wiki page	1298 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Killing–Hopf_theorem
is Link from a Wikipage to another Wikipage of	Spherical space form conjecture Constant curvature Wilhelm Killing Heinz Hopf Hyperbolic space List of theorems Space form Killing-Hopf theorem Hopf-Killing theorem Hopf–Killing theorem
is Wikipage redirect of	Killing-Hopf theorem Hopf-Killing theorem Hopf–Killing theorem
is known for of	Heinz Hopf
is known for of	Heinz Hopf
is foaf:primaryTopic of	wikipedia-en:Killing–Hopf_theorem

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