On the differentiable sphere theorem for manifolds with Ricci curvatures bounded from above

Abstract

In the present paper, we prove that if is an -dimensional compact Riemannian manifold and if where , and are the sectional and Ricci curvatures of respectively, then is diffeomorphic to a spherical space form where is a finite group of isometries acting freely. In particular, if is simply connected, then it is diffeo­mor­phic to the Euclidian sphere

Keywords

• riemannian manifold
• sectional curvature
• ricci curvatu­re
• sphere theorem
• spherical space form