A general theory of canonical forms

Palais, Richard S.; Terng, Chuu-Lian

doi:10.1090/S0002-9947-1987-0876478-4

A general theory of canonical forms
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by Richard S. Palais and Chuu-Lian Terng PDF

Trans. Amer. Math. Soc. 300 (1987), 771-789 Request permission

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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