, Volume 68, Issue 1, pp 405-415

Metrics of positive ricci curvature with large diameter

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Abstract

Examples are constructed of n-manifolds of positive Ricci curvature with almost maximal diameter, consistent with Myer's theorem, which are not homotopy equivalent to the n-sphere. This implies that the topological rigidity associated to the metric rigidity of Myer's theorem, fails in this case. Similar results hold for the estimate of the first eigenvalue of the Laplace operator.

Partially supported by an N.S.F. Grant