Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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
MathSciNet review: 906813
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 53C20, 53C30, 57R60, 57S25

Retrieve articles in all journals with MSC: 53C20, 53C30, 57R60, 57S25


Additional Information

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