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- Polar_action abstract "In mathematics, a polar action is a proper and isometric action of a Lie group G on a complete Riemannian manifold M for which there exists a complete submanifold Σ that meets all the orbits and meets them always orthogonally; such a submanifold is called a section. A section is necessarily totally geodesic. If the sections of a polar action are flat with respect to the induced metric, then the action is called hyperpolar.In the case of linear orthogonal actions on Euclidean spaces, polar actions are called polar representations. The isotropy representations of Riemannian symmetric spaces are basic examples of polar representations. Conversely, Dadok has classified polar representations of compact Lie groups on Euclidean spaces, and it follows from his classification that such a representation has the same orbits as the isotropy representation of a symmetric space.".
- Polar_action wikiPageID "19819949".
- Polar_action wikiPageLength "1355".
- Polar_action wikiPageOutDegree "13".
- Polar_action wikiPageRevisionID "601818925".
- Polar_action wikiPageWikiLink Category:Differential_geometry.
- Polar_action wikiPageWikiLink Euclidean_space.
- Polar_action wikiPageWikiLink Flat_manifold.
- Polar_action wikiPageWikiLink Glossary_of_Riemannian_and_metric_geometry.
- Polar_action wikiPageWikiLink Group_action.
- Polar_action wikiPageWikiLink Group_representation.
- Polar_action wikiPageWikiLink Isometry.
- Polar_action wikiPageWikiLink Lie_group.
- Polar_action wikiPageWikiLink Mathematics.
- Polar_action wikiPageWikiLink Orbit_(group_theory).
- Polar_action wikiPageWikiLink Riemannian_manifold.
- Polar_action wikiPageWikiLink Submanifold.
- Polar_action wikiPageWikiLink Symmetric_space.
- Polar_action wikiPageWikiLink Totally_geodesic.
- Polar_action wikiPageWikiLinkText "Polar action".
- Polar_action hasPhotoCollection Polar_action.
- Polar_action wikiPageUsesTemplate Template:Differential-geometry-stub.
- Polar_action wikiPageUsesTemplate Template:Multiple_issues.
- Polar_action subject Category:Differential_geometry.
- Polar_action hypernym Action.
- Polar_action type Article.
- Polar_action type MilitaryConflict.
- Polar_action type Article.
- Polar_action type Physic.
- Polar_action comment "In mathematics, a polar action is a proper and isometric action of a Lie group G on a complete Riemannian manifold M for which there exists a complete submanifold Σ that meets all the orbits and meets them always orthogonally; such a submanifold is called a section. A section is necessarily totally geodesic.".
- Polar_action label "Polar action".
- Polar_action sameAs m.04q1qt3.
- Polar_action sameAs Q7209059.
- Polar_action sameAs Q7209059.
- Polar_action wasDerivedFrom Polar_action?oldid=601818925.
- Polar_action isPrimaryTopicOf Polar_action.