The Radius Rigidity Theorem for Manifolds of Positive Curvature

Abstract

Recall that the radius of a compact metric space $(X,dist)$ is given by $radX={\min }_{x\in X}{\max }_{y\in X}dist(x,y)$. In this paper we generalize Berger's $\frac{1}{4}$-pinched rigidity theorem and show that a closed, simply connected, Riemannian manifold with sectional curvature $\ge 1$ and radius $\ge \frac{\pi }{2}$ is either homeomorphic to the sphere or isometric to a compact rank one symmetric space.

arXiv comment29 pages, latex, no figures

Cited by in corpus (1)

• Great sphere foliations and manifolds with curvature bounded above