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Transactions of the American Mathematical Society

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Equivariant geometry and Kervaire spheres


Authors: Allen Back and Wu-Yi Hsiang
Journal: Trans. Amer. Math. Soc. 304 (1987), 207-227
MSC: Primary 53C20; Secondary 53C30, 57R60, 57S25
DOI: https://doi.org/10.1090/S0002-9947-1987-0906813-X
MathSciNet review: 906813
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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.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1987-0906813-X
Article copyright: © Copyright 1987 American Mathematical Society

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