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

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

2006-01-31

arxiv.org/abs/math/0601765v1

Mathematics

Differential Geometry

10 pages

Scientific paper

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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