Non-negative curvature obstructions in cohomogeneity one and the Kervaire spheres

2006/01/31 by Karsten Grove, Grove, K., Burkhard Wilking +5 · 1 citation
Mathematics · #53C20 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0601765

openalex publication_date 2006/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In contrast to the homogeneous case, we show that there are compact cohomogeneity one manifolds, that do not support invariant metrics of non-negative sectional curvature. In fact we exhibit infinite families of such manifolds including the exotic Kervaire spheres. Such examples exist for any codimension of the singular orbits except for the case where both are equal to two, where existence of non-negatively curved metrics is known.

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