Curvature, sphere theorems, and the Ricci flow |
Abstract:
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: alexsuciu@neu.edu | |
Posted: September 24, 2010 | URL: http://www.math.neu.edu/bhmn/brendle10.html |