THE RADIUS RIGIDITY THEOREM FOR MANIFOLDS OF POSITIVE CURVATURE

Recall that the radius of a compact metric space (X,dist) is given by rad X = min(x is an element of X) max(y is an element of X) dist(x,y). In this paper we generalize Berger's 1/4-pinched rigidity theorem and show that a closed, simply connected, Riemannian manifold with sectio nal curvature greater than or equal to 1 and radius greater than or eq ual to pi/2 is either homeomorphic to the sphere or isometric to a com pact rank-one symmetric space.