sphere theorem from global differential geometry

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

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

 $0

Then $M$ is homeomorphic to a sphere.

References

• 1 M. P. do Carmo, Riemannian Geometry, Birkhäuser, Boston, 1992.
Title sphere theorem from global differential geometry SphereTheoremFromGlobalDifferentialGeometry 2013-03-22 15:54:09 2013-03-22 15:54:09 juanman (12619) juanman (12619) 8 juanman (12619) Theorem msc 53C21 msc 53C20 Curvature Connection