Der Sphärensatz in der Riemannschen Geometrie (Q642088)

The interplay between curvature and topology of a Riemannian manifold is a central problem in differential geometry. Based on a classical result of Heinz Hopf, a basic question is whether a compact simply-connected Riemannian manifold with sectional curvatures in \([1-\varepsilon,1]\) is a topological sphere. After a historical review, the author discusses the differentiable sphere theorem as well as some related results. For details, see the monograph of the author in [Ricci flow and the sphere theorem. Graduate Studies in Mathematics 111. Providence, RI: American Mathematical Society (AMS). vii, 176 p. (2010; Zbl 1196.53001)].