|Curvature, sphere theorems, and the Ricci flow|
In 1926, Hopf proved that any compact, simply connected Riemannian manifold with constant curvature 1
is isometric to the standard sphere. Motivated by this result, Hopf posed the question of
whether a compact, simply connected manifold with suitably pinched curvature is topologically a sphere.
This question has been studied by many authors over the past six decades, a milestone being
the Topological Sphere Theorem proved by Berger and Klingenberg in 1960.
|Web page: Alexandru I. Suciu||Comments to: firstname.lastname@example.org|
|Posted: September 24, 2010||URL: http://www.math.neu.edu/bhmn/brendle10.html|