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- Rauch_comparison_theorem abstract "In Riemannian geometry, the Rauch comparison theorem, named after Harry Rauch who proved it in 1951, is a fundamental result which relates the sectional curvature of a Riemannian manifold to the rate at which geodesics spread apart. Intuitively, it states that for positive curvature, geodesics tend to converge, while for negative curvature, geodesics tend to spread. This theorem is formulated using Jacobi fields to measure the variation in geodesics.".
- Rauch_comparison_theorem wikiPageID "16221737".
- Rauch_comparison_theorem wikiPageLength "1958".
- Rauch_comparison_theorem wikiPageOutDegree "11".
- Rauch_comparison_theorem wikiPageRevisionID "682216926".
- Rauch_comparison_theorem wikiPageWikiLink Category:Theorems_in_Riemannian_geometry.
- Rauch_comparison_theorem wikiPageWikiLink Conjugate_points.
- Rauch_comparison_theorem wikiPageWikiLink Geodesic.
- Rauch_comparison_theorem wikiPageWikiLink Harry_Rauch.
- Rauch_comparison_theorem wikiPageWikiLink Jacobi_field.
- Rauch_comparison_theorem wikiPageWikiLink Manfredo_do_Carmo.
- Rauch_comparison_theorem wikiPageWikiLink Riemannian_geometry.
- Rauch_comparison_theorem wikiPageWikiLink Riemannian_manifold.
- Rauch_comparison_theorem wikiPageWikiLink Sectional_curvature.
- Rauch_comparison_theorem wikiPageWikiLink Toponogovs_theorem.
- Rauch_comparison_theorem wikiPageWikiLinkText "Rauch comparison theorem".
- Rauch_comparison_theorem wikiPageUsesTemplate Template:Differential-geometry-stub.
- Rauch_comparison_theorem wikiPageUsesTemplate Template:Expert.
- Rauch_comparison_theorem subject Category:Theorems_in_Riemannian_geometry.
- Rauch_comparison_theorem hypernym Result.
- Rauch_comparison_theorem type Theorem.
- Rauch_comparison_theorem comment "In Riemannian geometry, the Rauch comparison theorem, named after Harry Rauch who proved it in 1951, is a fundamental result which relates the sectional curvature of a Riemannian manifold to the rate at which geodesics spread apart. Intuitively, it states that for positive curvature, geodesics tend to converge, while for negative curvature, geodesics tend to spread. This theorem is formulated using Jacobi fields to measure the variation in geodesics.".
- Rauch_comparison_theorem label "Rauch comparison theorem".
- Rauch_comparison_theorem sameAs Q7296106.
- Rauch_comparison_theorem sameAs m.03wd8l3.
- Rauch_comparison_theorem sameAs Теорема_сравнения_Рауха.
- Rauch_comparison_theorem sameAs Q7296106.
- Rauch_comparison_theorem wasDerivedFrom Rauch_comparison_theorem?oldid=682216926.
- Rauch_comparison_theorem isPrimaryTopicOf Rauch_comparison_theorem.