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geometry > differential geometry > Riemannian geometry > sphere theorem

Terme préférentiel

sphere theorem  

Définition(s)

  • 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 is a complete, simply-connected, n-dimensional Riemannian manifold with sectional curvature taking values in the interval (1,4] then M is homeomorphic to the n-sphere. (To be precise, we mean the sectional curvature of every tangent 2-plane at each point must lie in (1,4].) Another way of stating the result is that if M is not homeomorphic to the sphere, then it is impossible to put a metric on M with quarter-pinched curvature.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Sphere_theorem)

Concept(s) générique(s)

Synonyme(s)

  • quarter-pinched sphere theorem

Traductions

URI

http://data.loterre.fr/ark:/67375/PSR-MZ0GN0F0-S

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