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- Myers–Steenrod_theorem abstract "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 (i.e., 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).".
- Myers–Steenrod_theorem wikiPageExternalLink S0002-9939-1957-0088000-X.
- Myers–Steenrod_theorem wikiPageExternalLink 1968928.
- Myers–Steenrod_theorem wikiPageID "33844541".
- Myers–Steenrod_theorem wikiPageLength "1597".
- Myers–Steenrod_theorem wikiPageOutDegree "19".
- Myers–Steenrod_theorem wikiPageRevisionID "573271787".
- Myers–Steenrod_theorem wikiPageWikiLink Category:Theorems_in_Riemannian_geometry.
- Myers–Steenrod_theorem wikiPageWikiLink Connectedness.
- Myers–Steenrod_theorem wikiPageWikiLink Continuous_function.
- Myers–Steenrod_theorem wikiPageWikiLink Differentiable_function.
- Myers–Steenrod_theorem wikiPageWikiLink Isometry.
- Myers–Steenrod_theorem wikiPageWikiLink Isometry_(Riemannian_geometry).
- Myers–Steenrod_theorem wikiPageWikiLink Isometry_group.
- Myers–Steenrod_theorem wikiPageWikiLink Lie_group.
- Myers–Steenrod_theorem wikiPageWikiLink Mathematics.
- Myers–Steenrod_theorem wikiPageWikiLink Metric_space.
- Myers–Steenrod_theorem wikiPageWikiLink Norman_Steenrod.
- Myers–Steenrod_theorem wikiPageWikiLink Orthogonal_group.
- Myers–Steenrod_theorem wikiPageWikiLink Richard_Palais.
- Myers–Steenrod_theorem wikiPageWikiLink Riemannian_geometry.
- Myers–Steenrod_theorem wikiPageWikiLink Riemannian_manifold.
- Myers–Steenrod_theorem wikiPageWikiLink Smoothness.
- Myers–Steenrod_theorem wikiPageWikiLink Sphere.
- Myers–Steenrod_theorem wikiPageWikiLink Sumner_Byron_Myers.
- Myers–Steenrod_theorem wikiPageWikiLink Theorem.
- Myers–Steenrod_theorem wikiPageWikiLinkText "Myers–Steenrod theorem".
- Myers–Steenrod_theorem wikiPageUsesTemplate Template:Citation.
- Myers–Steenrod_theorem subject Category:Theorems_in_Riemannian_geometry.
- Myers–Steenrod_theorem type Redirect.
- Myers–Steenrod_theorem type Theorem.
- Myers–Steenrod_theorem comment "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 (i.e., 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.".
- Myers–Steenrod_theorem label "Myers–Steenrod theorem".
- Myers–Steenrod_theorem sameAs Q6947443.
- Myers–Steenrod_theorem sameAs Stelling_van_Myers-Steenrod.
- Myers–Steenrod_theorem sameAs m.0hndvkr.
- Myers–Steenrod_theorem sameAs Q6947443.
- Myers–Steenrod_theorem wasDerivedFrom Myers–Steenrod_theorem?oldid=573271787.
- Myers–Steenrod_theorem isPrimaryTopicOf Myers–Steenrod_theorem.