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- Myers's_theorem abstract "The Myers theorem, also known as the Bonnet–Myers theorem, is a classical theorem in Riemannian geometry. The strong form was proven by Sumner Byron Myers. The theorem states that if Ricci curvature of a complete Riemannian manifold M is bounded below by (n − 1)k > 0, then its diameter is at most π/√k. The weaker result, due to Ossian Bonnet, has the same conclusion but under the stronger assumption that the sectional curvatures be bounded below by k.Moreover, if the diameter is equal to π/√k, then the manifold is isometric to a sphere of a constant sectional curvature k. This rigidity result is due to Cheng (1975), and is often known as Cheng's theorem.This result also holds for the universal cover of such a Riemannian manifold, in particular both M and its cover are compact, so the cover is finite-sheeted and M has finite fundamental group.".
- Myers's_theorem wikiPageID "932460".
- Myers's_theorem wikiPageRevisionID "553481771".
- Myers's_theorem hasPhotoCollection Myers's_theorem.
- Myers's_theorem subject Category:Geometric_inequalities.
- Myers's_theorem subject Category:Theorems_in_Riemannian_geometry.
- Myers's_theorem type Abstraction100002137.
- Myers's_theorem type Attribute100024264.
- Myers's_theorem type Communication100033020.
- Myers's_theorem type Difference104748836.
- Myers's_theorem type GeometricInequalities.
- Myers's_theorem type Inequality104752221.
- Myers's_theorem type Message106598915.
- Myers's_theorem type Proposition106750804.
- Myers's_theorem type Quality104723816.
- Myers's_theorem type Statement106722453.
- Myers's_theorem type Theorem106752293.
- Myers's_theorem type TheoremsInGeometry.
- Myers's_theorem type TheoremsInRiemannianGeometry.
- Myers's_theorem comment "The Myers theorem, also known as the Bonnet–Myers theorem, is a classical theorem in Riemannian geometry. The strong form was proven by Sumner Byron Myers. The theorem states that if Ricci curvature of a complete Riemannian manifold M is bounded below by (n − 1)k > 0, then its diameter is at most π/√k.".
- Myers's_theorem label "Myers's theorem".
- Myers's_theorem label "Satz von Bonnet-Myers".
- Myers's_theorem label "Stelling van Myers".
- Myers's_theorem label "Théorème de Bonnet-Schoenberg-Myers".
- Myers's_theorem label "邁爾斯定理".
- Myers's_theorem sameAs Satz_von_Bonnet-Myers.
- Myers's_theorem sameAs Théorème_de_Bonnet-Schoenberg-Myers.
- Myers's_theorem sameAs Stelling_van_Myers.
- Myers's_theorem sameAs m.03r70m.
- Myers's_theorem sameAs Q929547.
- Myers's_theorem sameAs Q929547.
- Myers's_theorem sameAs Myers's_theorem.
- Myers's_theorem wasDerivedFrom Myers's_theorem?oldid=553481771.
- Myers's_theorem isPrimaryTopicOf Myers's_theorem.