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 be a n-dimensional compact simply connected Riemannian manifold, whose sectional curvature
satisfies
Then is homeomorphic to a sphere.
References
- 1 M. P. do Carmo, Riemannian Geometry, Birkhäuser, Boston, 1992.