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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 wikiPageRevisionID "578643919".
- Rauch_comparison_theorem hasPhotoCollection Rauch_comparison_theorem.
- Rauch_comparison_theorem subject Category:Theorems_in_Riemannian_geometry.
- Rauch_comparison_theorem type Abstraction100002137.
- Rauch_comparison_theorem type Communication100033020.
- Rauch_comparison_theorem type Message106598915.
- Rauch_comparison_theorem type Proposition106750804.
- Rauch_comparison_theorem type Statement106722453.
- Rauch_comparison_theorem type Theorem106752293.
- Rauch_comparison_theorem type TheoremsInGeometry.
- Rauch_comparison_theorem type TheoremsInRiemannianGeometry.
- 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 m.03wd8l3.
- Rauch_comparison_theorem sameAs Q7296106.
- Rauch_comparison_theorem sameAs Q7296106.
- Rauch_comparison_theorem sameAs Rauch_comparison_theorem.
- Rauch_comparison_theorem wasDerivedFrom Rauch_comparison_theorem?oldid=578643919.
- Rauch_comparison_theorem isPrimaryTopicOf Rauch_comparison_theorem.