About: Myers–Steenrod theorem

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Two theorems in the mathematical field of Riemannian geometry bear the name Myers–Steenrod theorem, both from a 1939 paper by Myers and Steenrod. The first states that every distance-preserving map (that is, an isometry of metric spaces) between two connected Riemannian manifolds is actually a smooth isometry of Riemannian manifolds. A simpler proof was subsequently given by Richard Palais in 1957. The main difficulty lies in showing that a distance-preserving map, which is a priori only continuous, is actually differentiable.

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rdf:type	yago:WikicatTheoremsInRiemannianGeometry yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293
rdfs:label	Satz von Myers-Steenrod (de) Myers–Steenrod theorem (en) Stelling van Myers-Steenrod (nl) Теорема Майерса — Стинрода (ru)
rdfs:comment	Der Satz von Myers-Steenrod ist ein Lehrsatz aus dem mathematischen Gebiet der Differentialgeometrie. Er besagt, dass die Isometriegruppe jeder vollständigen Riemannschen Mannigfaltigkeit eine Lie-Gruppe ist. Ihre Dimension ist höchstens . Der Satz stammt von Norman Steenrod und Sumner Byron Myers. (de) In de Riemann-meetkunde, een deelgebied van de wiskunde, dragen twee stellingen de naam stelling van Myers-Steenrod. Beide hebben hun naam te danken aan een artikel uit 1939 van de wiskundigen en . (nl) Теорема Майерса — Стинрода — пара тесно связанных классических утверждений о группе изометрий риманова многообразия. (ru) Two theorems in the mathematical field of Riemannian geometry bear the name Myers–Steenrod theorem, both from a 1939 paper by Myers and Steenrod. The first states that every distance-preserving map (that is, an isometry of metric spaces) between two connected Riemannian manifolds is actually a smooth isometry of Riemannian manifolds. A simpler proof was subsequently given by Richard Palais in 1957. The main difficulty lies in showing that a distance-preserving map, which is a priori only continuous, is actually differentiable. (en)
dcterms:subject	Theorems in Riemannian geometry Differential geometry
Wikipage page ID	33844541 (xsd:integer)
Wikipage revision ID	1053923229 (xsd:integer)
Link from a Wikipage to another Wikipage	Theorems in Riemannian geometry Riemannian manifolds Lie group Isometry (Riemannian geometry) Differential geometry Connected space Theorems Smooth function Richard Palais Norman Steenrod Isometry group Continuity (topology) Riemannian geometry Isometry Sumner Byron Myers Differentiable function Sphere Metric space Orthogonal group Mathematical
sameAs	Myers–Steenrod theorem Myers–Steenrod theorem Myers–Steenrod theorem Myers–Steenrod theorem Myers–Steenrod theorem Myers–Steenrod theorem
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Reflist dbt:Short_description dbt:Manifolds
has abstract	Der Satz von Myers-Steenrod ist ein Lehrsatz aus dem mathematischen Gebiet der Differentialgeometrie. Er besagt, dass die Isometriegruppe jeder vollständigen Riemannschen Mannigfaltigkeit eine Lie-Gruppe ist. Ihre Dimension ist höchstens . Der Satz stammt von Norman Steenrod und Sumner Byron Myers. (de) Two theorems in the mathematical field of Riemannian geometry bear the name Myers–Steenrod theorem, both from a 1939 paper by Myers and Steenrod. The first states that every distance-preserving map (that is, an isometry of metric spaces) between two connected Riemannian manifolds is actually a smooth isometry of Riemannian manifolds. A simpler proof was subsequently given by Richard Palais in 1957. The main difficulty lies in showing that a distance-preserving map, which is a priori only continuous, is actually differentiable. The second theorem, which is much more difficult to prove, states that the isometry group of a Riemannian manifold is a Lie group. For instance, the group of isometries of the two-dimensional unit sphere is the orthogonal group O(3). (en) In de Riemann-meetkunde, een deelgebied van de wiskunde, dragen twee stellingen de naam stelling van Myers-Steenrod. Beide hebben hun naam te danken aan een artikel uit 1939 van de wiskundigen en . (nl) Теорема Майерса — Стинрода — пара тесно связанных классических утверждений о группе изометрий риманова многообразия. (ru)
prov:wasDerivedFrom	wikipedia-en:Myers–Steenrod_theorem?oldid=1053923229&ns=0
page length (characters) of wiki page	1751 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Myers–Steenrod_theorem
is Link from a Wikipage to another Wikipage of	Isometry Sumner Byron Myers Myers-Steenrod theorem
is Wikipage redirect of	Myers-Steenrod theorem
is known for of	Sumner Byron Myers
is known for of	Sumner Byron Myers
is foaf:primaryTopic of	wikipedia-en:Myers–Steenrod_theorem

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