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 manifoldMathworldPlanetmath, whose sectional curvatureMathworldPlanetmath K satisfies


Then M is homeomorphic to a sphere.


  • 1 M. P. do Carmo, Riemannian Geometry, Birkhäuser, Boston, 1992.
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 CurvaturePlanetmathPlanetmath
Related topic ConnectionMathworldPlanetmath