Equivariant geometry and Kervaire spheres

Back, Allen; Hsiang, Wu-Yi

doi:10.1090/S0002-9947-1987-0906813-X

Equivariant geometry and Kervaire spheres
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by Allen Back and Wu-Yi Hsiang

Trans. Amer. Math. Soc. 304 (1987), 207-227

DOI: https://doi.org/10.1090/S0002-9947-1987-0906813-X

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Abstract:

The intrinsic geometry of metrics on the Kervaire sphere which are invariant under a large transformation group (cohomogeneity one) is studied. Invariant theory is used to describe the behavior of these metrics near the singular orbits. Nice expressions for the Ricci and sectional curvatures are obtained. The nonexistence of invariant metrics of positive sectional curvature is proven, and Cheeger’s construction of metrics of positive Ricci curvature is discussed.

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