Curvature and cohomogeneity one
Lorenz J. Schwachhöfer and Wilderich Tuschmann
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Submission date: 24. Sep. 2001
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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.