sphere theorem from global differential geometry

This theorem, as do Carmo refers it, is one of the most beautiful theorems in Riemannian geometry:

sphere theorem. Let $M$ be a n-dimensional compact simply connected Riemannian manifold, whose sectional curvature $K$ satisfies

Then $M$ is homeomorphic to a sphere.

Title	sphere theorem from global differential geometry
Canonical name	SphereTheoremFromGlobalDifferentialGeometry
Date of creation	2013-03-22 15:54:09
Last modified on	2013-03-22 15:54:09
Owner	juanman (12619)
Last modified by	juanman (12619)
Numerical id	8
Author	juanman (12619)
Entry type	Theorem
Classification	msc 53C21
Classification	msc 53C20
Related topic	Curvature
Related topic	Connection