Manifolds with almost non-negative curvature
by
Lorenz Schwachhöfer
Université Libre de Bruxelles

A (closed) manifold M is said to have almost non-negative curvature if there exists a sequence of Riemannian metrics on M with fixed diameter whose lower curvature bound is arbitrarily close to zero.

We shall present some new examples of almost non-negatively curved manifolds. All of these are cohomogeneity one, i.e. they admit a smooth group action whose maximal orbit has codimension one. These examples include the Kevaire spheres, i.e. certain odd-dimensional exotic spheres.

Date received: February 22, 2001