The number of exceptional orbits of a pseudofree circle action on S(5)

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Let M be a closed Riemannian manifold of dimension 5 which admits a Riemannian metric of nonnegative sectional curvature. The aim of this short paper is to show that under certain lower bound of the orders of isotropy subgroups, every pseudofree and isometric S-1-action on M cannot have more than five exceptional circle orbits. As a consequence, we conclude that a pseudofree and isometric S-1-action on a 5-sphere S-5 with a Riemannian metric of nonnegative sectional curvature cannot have more than five exceptional circle orbits. This gives a result related to the Montgomery-Yang problem. In addition, we also give some further related result about nonnegatively curved manifolds of dimension 5 with an isometric but not necessarily pseudofree circle action.
Publisher
BIRKHAUSER VERLAG AG
Issue Date
2011-03
Language
English
Article Type
Article
Keywords

SYMMETRY; TOPOLOGY; 4-MANIFOLDS

Citation

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, v.9, no.1, pp.55 - 62

ISSN
1661-7738
URI
http://hdl.handle.net/10203/98427
Appears in Collection
MA-Journal Papers(저널논문)
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