A DIFFERENTIABLE SPHERE THEOREM BY CURVATURE PINCHING II

Dedicated to Professor Shoshichi Kobayashi on his sixtieth birthday

Abstract

We give a new diffeotopy theorem on the standard sphere, and an estimate for some geometric invariants concerning positively curved Riemannian manifold. By using these results we prove that a complete, simply connected and 0.654-pinched Riemannian manifold is diffeomorphic to the standard sphere.