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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

A general theory of canonical forms


Authors: Richard S. Palais and Chuu-Lian Terng
Journal: Trans. Amer. Math. Soc. 300 (1987), 771-789
MSC: Primary 57S15; Secondary 53C20, 58E30
MathSciNet review: 876478
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Abstract: If $ G$ is a compact Lie group and $ M$ a Riemannian $ G$-manifold with principal orbits of codimension $ k$ then a section or canonical form for $ M$ is a closed, smooth $ k$-dimensional submanifold of $ M$ which meets all orbits of $ M$ orthogonally. We discuss some of the remarkable properties of $ G$-manifolds that admit sections, develop methods for constructing sections, and consider several applications.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0876478-4
PII: S 0002-9947(1987)0876478-4
Article copyright: © Copyright 1987 American Mathematical Society