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Sphere theorem

In Riemannian geometry, the sphere theorem, also known as the quarter-pinched sphere theorem, strongly restricts the topology of manifolds admitting metrics with a particular curvature bound. The precise statement of the theorem is as follows. If M {\displaystyle M} is a complete, simply-connected, n-dimensional Riemannian manifold with sectional…

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Differentiable sphere theorem

History of the sphere theorem

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Sphere theorem

Nodes24
Edges23
Triples37
Avg. degree1.92
Density0.083333
Components1

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Sphere theorem

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related to References · 19
Sphere theorem → American Mathematical Society, Bibcode, Brendle, Bulletin, Curvature, Graduate Studies, ISBN, Journal, Manifolds, Mathematics, MR, Providence, RI, Ricci Flow, Richard, Schoen, Simon, Sphere Theorems, Vol
related to Differentiable sphere theorem · 10
Sphere theorem → Brendle, For, However, Moreover, Ricci, Richard Schoen, Schoen, Simon Brendle, The, This
related to history · 8
Sphere theorem → Berger, Harry Rauch, Heinz Hopf, In, Marcel Berger, Panoramic View, Riemannian Geometry, Wilhelm Klingenberg

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sphere displaystyle theorem curvature sectional values homeomorphic brendle riemannian n-sphere simon schoen manifold quarter-pinched precise interval metric curvatures take diffeomorphic

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SubjectPredicateObjectConfidenceSrc
Sphere theoremrelated to Differentiable sphere theoremThe0.60section
Sphere theoremrelated to Differentiable sphere theoremThis0.60section
Sphere theoremrelated to Differentiable sphere theoremFor0.60section
Sphere theoremrelated to Differentiable sphere theoremHowever0.60section
Sphere theoremrelated to Differentiable sphere theoremSimon Brendle0.60section
Sphere theoremrelated to Differentiable sphere theoremRichard Schoen0.60section
Sphere theoremrelated to Differentiable sphere theoremRicci0.60section
Sphere theoremrelated to Differentiable sphere theoremMoreover0.60section
Sphere theoremrelated to Differentiable sphere theoremBrendle0.60section
Sphere theoremrelated to Differentiable sphere theoremSchoen0.60section
Sphere theoremrelated to historyHeinz Hopf0.60section
Sphere theoremrelated to historyIn0.60section

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