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- 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)
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- 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)
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- Satz von Myers-Steenrod (de)
- Myers–Steenrod theorem (en)
- Stelling van Myers-Steenrod (nl)
- Теорема Майерса — Стинрода (ru)
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