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MiS Preprint
62/2001

Curvature and cohomogeneity one

Lorenz J. Schwachhöfer and Wilderich Tuschmann

Abstract

We show that any closed cohomogeneity one manifold supports metrics of almost nonnegative sectional curvature which are moreover invariant under the cohomogeneity one action, thereby establishing a conjecture of Grove and Ziller in the almost nonnegatively curved setting. Applications of our result include that there are infinitely many dimensions in which there exist almost nonnegatively curved topological spheres and homotopy lens as well as homotopy real projective spaces, all differentiably distinct from the standard ones.

Received:
Sep 24, 2001
Published:
Sep 24, 2001

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Preprint
2001 Repository Open Access
Lorenz J. Schwachhöfer and Wilderich Tuschmann

Curvature and cohomogeneity one