Keywords

#sphere_theorem

Sphere theorem

On when a Riemannian manifold with sectional curvature in the interval (1, 4] is a sphere

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 then M is homeomorphic to the n-sphere. 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.

Wed 31st

Provided by Wikipedia

Learn More

This keyword could refer to multiple things. Here are some suggestions:

Sphere theorem Shell theorem Hairy ball theorem 3-manifold Uniformization theorem Richard Schoen Pythagorean theorem Reeb sphere theorem Simon Brendle Poincaré–Hopf theorem
0 searches
This keyword has never been searched before
This keyword has never been searched for with any other keyword.