The Journal of Geometric Analysis

, Volume 11, Issue 3, pp 519–560

An exotic sphere with positive curvature almost everywhere


DOI: 10.1007/BF02922018

Cite this article as:
Wilhelm, F. J Geom Anal (2001) 11: 519. doi:10.1007/BF02922018


In this article we show that there is an exotic sphere with positive sectional curvature almost everywhere.

In 1974 Gromoll and Meyer found a metric of nonnegative sectional on an exotic 7-sphere. They showed that the metric has positive curvature at a point and asserted, without proof, that the metric has positive sectional curvature almost everywhere [4]. We will show here that this assertion is wrong. In fact, the Gromoll-Meyer sphere has zero curvatures on an open set of points. Never the less, its metric can be perturbed to one that has positive curvature almost everywhere.

Math Subject Classifications


Key Words and Phrases

exotic spherepositive curvature

Copyright information

© Mathematica Josephina, Inc. 2001

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaRiverside